fault-tolerant topology control in heterogeneous wireless …

FAULT-TOLERANT TOPOLOGY CONTROL IN HETEROGENEOUS WIRELESSSENSOR NETWORKS

A THESIS SUBMITTED TOTHE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OFMIDDLE EAST TECHNICAL UNIVERSITY

HAKKI BAGCI

IN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR

THE DEGREE OF DOCTOR OF PHILOSOPHYIN

COMPUTER ENGINEERING

OCTOBER 2013

Approval of the thesis:


submitted by HAKKI BAGCI in partial fulfillment of the requirements for the degree of Doc-tor of Philosophy in Computer Engineering Department, Middle East Technical Univer-sity by,

Prof. Dr. Canan ÖzgenDean, Graduate School of Natural and Applied Sciences

Prof. Dr. Adnan YazıcıHead of Department, Computer Engineering

Prof. Dr. Adnan YazıcıSupervisor, Computer Engineering Dept., METU

Assoc. Prof. Dr. Ibrahim KörpeogluCo-supervisor, Computer Engineering Dept., Bilkent University

Examining Committee Members:

Prof. Dr. Özgür UlusoyComputer Engineering Dept., Bilkent University

Prof. Dr. Adnan YazıcıComputer Engineering Dept., METU

Assoc. Prof. Dr. Ahmet CosarComputer Engineering Dept., METU

Assist. Prof. Dr. Erhan ErenInformatics Institute, METU

Assist. Prof. Dr. Ahmet Oguz AkyüzComputer Engineering Dept., METU

Date:

I hereby declare that all information in this document has been obtained and presentedin accordance with academic rules and ethical conduct. I also declare that, as requiredby these rules and conduct, I have fully cited and referenced all material and results thatare not original to this work.

Name, Last Name: HAKKI BAGCI

Signature :

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ABSTRACT


Bagcı, Hakkı

Ph.D., Department of Computer Engineering

Supervisor : Prof. Dr. Adnan Yazıcı

Co-Supervisor : Assoc. Prof. Dr. Ibrahim Körpeoglu

October 2013, 83 pages

Wireless sensor networks have come into prominence for monitoring and tracking opera-tions in many application areas including environmental monitoring, battlefield surveillance,healthcare solutions, vehicle traffic monitoring, smart home systems and many other indus-trial applications. A long network life time and fault-tolerant operation are two essentialrequirements for wireless sensor network applications. In order to satisfy these requirements,heterogeneous architectures can be employed in wireless sensor network applications, wherethe network consists of several layers that are composed of different types of nodes instead ofa homogeneous flat topology. In order to address energy efficient and fault-tolerant topologycontrol in heterogeneous wireless sensor networks, we propose a distributed, energy efficientand fault-tolerant topology control algorithm called the Disjoint Path Vector (DPV), whichfinds disjoint paths from each sensor node to set of supernodes. We prove the correctness ofour approach by showing that topologies generated by DPV are guaranteed to satisfy k-vertexsupernode connectivity. Our simulations show that the DPV algorithm can achieve a 4-foldreduction in total transmission power and a 2-fold reduction in maximum transmission powercompared to existing solutions. Under realistic packet loss scenarios our algorithm can reach60% decrease in total transmission power.

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Keywords: Heterogeneous Wireless Sensor Networks, Topology Control, Fault Tolerance,Energy Efficiency, Disjoint Paths

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ÖZ

HETEROJEN KABLOSUZ DUYARGA AGLARINDA HATA TOLERANSLI TOPOLOJIKONTROL

Bagcı, Hakkı

Doktora, Bilgisayar Mühendisligi Bölümü Bölümü

Tez Yöneticisi : Prof. Dr. Adnan Yazıcı

Ortak Tez Yöneticisi : Assoc. Prof. Dr. Ibrahim Körpeoglu

Ekim 2013 , 83 sayfa

Kablosuz duyarga agları, gözlemleme ve takip operasyonlarında çevre gözlemleme, savasalanı gözetleme, saglık çözümleri, trafik izleme, akıllı ev sistemleri ve diger bir çok endüst-riyel uygulamalar için önem kazanmaktadır. Kablosuz duyarga agları uygulamalarının en be-lirgin isterleri mümkün oldugunca uzun ömürlü olmaları ve bu tip aglarda sıkça görülen hata-lara karsı da tolerans gösterebilmeleridir. Bu isterleri saglamak amacıyla düz mimariler yerinefarklı özelliklere sahip dügümlerden olusan heterojen mimariler kullanılabilmektedir. Bu tezçalısmasında heterojen yapılı kablosuz duyarga aglarında enerji etkin ve hataya toleranslı to-poloji kontrol problemine çözüm olarak agda yer alan her dügümden süper dügüm kümesineayrık yollar bulan dagıtık, enerji etkin ve hataya toleranslı bir topoloji kontrol algoritması(Disjoint Path Vector) öneriyoruz. Algoritmamızın hata toleransı için gerekli olan baglanır-lık seviyesini garanti ettigini ispat ediyoruz. Yaptıgımız simülasyonlar DPV algoritmasınınvar olan çözümlerden dügümlerin toplam çıkıs gücü açısından 4 kat, maksimum çıkıs gücüaçısından 2 kat daha etkin olabilecegini göstermektedir. Olası paket kaybı senaryolarında al-goritmamız diger çözümlere göre 60% daha düsük toplam çıkıs gücü elde edebilmektedir.

Anahtar Kelimeler: Heterojen Kablosuz Duyarga Agları, Topoloji Kontrol, Hata Toleransı,

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Enerji Etkin, Ayrık Yollar

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I dedicate this thesis to

my family,

my wife, Figen,

and my daughter, Ipek.

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ACKNOWLEDGMENTS

First and foremost I want to thank my supervisor Prof. Dr. Adnan Yazıcı for all the support

and encouragement he gave me. His guidance and positive approach throughout this time

period made possible to complete this work.

I would like to express my gratitude and profound respect to my co-advisor Assoc. Prof. Dr.

Ibrahim Körpeoglu for his suggestions, efforts and patience during this study. He has made

invaluable contributions to my academic studies since we started to work together in 2004.

I acknowledge with thanks and appreciation the members of thesis monitoring comittee, Prof.

Dr. Müslim Bozyigit, Assist. Prof. Dr. Erhan Eren and Assist. Prof. Dr. Ahmet Oguz Akyüz.

Their advice helped me to move forward in this study.

I thank to the members of the thesis jury, Prof. Dr. Özgür Ulusoy and Assoc. Prof. Dr. Ahmet

Cosar for reviewing and evaluating my thesis.

I also thank to TUBITAK / BILGEM / ILTAREN for supporting my academic studies.

Special thanks go to my unit director at ILTAREN, Dr. Alper Yıldırım for the support and

encouragement he gave me during my PhD studies.

I thank to my wife, for her understanding and support during my thesis study.

Finally, I would like to express my thanks to my parents and brother for their love, trust and

every kind of supports.

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TABLE OF CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

ÖZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

CHAPTERS

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Overview of Wireless Sensor Networks . . . . . . . . . . . . . . . . 3

2.2 Heterogeneous Wireless Sensor Networks . . . . . . . . . . . . . . 5

2.3 Topology Control in Wireless Sensor Networks . . . . . . . . . . . 6

2.3.1 Geometrical Structures . . . . . . . . . . . . . . . . . . . 8

2.3.1.1 RNG and GG . . . . . . . . . . . . . . . . . 8

2.3.1.2 Minimum Spanning Tree . . . . . . . . . . . 9

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2.3.1.3 Delaunay Triangulation . . . . . . . . . . . . 9

2.3.1.4 Bounded Degree Spanners . . . . . . . . . . 9

2.3.1.5 Virtual Backbones . . . . . . . . . . . . . . . 11

2.4 Fault Tolerance in Wireless Sensor Networks . . . . . . . . . . . . . 12

3 RELATED WORK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 PROPOSED WORK: DISJOINT PATH VECTOR ALGORITHM . . . . . . 25

4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Sample Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.4 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.5 Disjoint Path Vector Algorithm for k-vertex Supernode Connectivity 28

4.6 Time Complexity Analysis of the DPV Algorithm . . . . . . . . . . 44

4.7 Message Complexity Analysis of the DPV Algorithm . . . . . . . . 47

5 EVALUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.1 Evaluation Approach . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.3.1 Total Transmission Power . . . . . . . . . . . . . . . . . 52

5.3.2 Maximum transmission power . . . . . . . . . . . . . . . 54

5.3.3 Total number of links . . . . . . . . . . . . . . . . . . . . 55

5.3.4 Total Number of Control Message Transmissions . . . . . 63

5.3.5 Total Number of Control Message Receptions . . . . . . . 63

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5.3.6 Effect of Packet Losses . . . . . . . . . . . . . . . . . . . 68

6 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

CURRICULUM VITAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

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LIST OF TABLES

TABLES

Table 4.1 Path Information Table at node y. Node y holds 3 paths to supernodes. . . . 29

Table 4.2 DPV Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Table 4.3 Time and message complexities of DPV and DATC per node. . . . . . . . . 47

Table 5.1 Simulation Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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LIST OF FIGURES

FIGURES

Figure 2.1 RNG, GG and Delaunay Triangulation. . . . . . . . . . . . . . . . . . . . 10

Figure 2.2 Yao Graph Formation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Figure 3.1 Initially node a’s transmission range is set as to reach its k closest neighbors. 21

Figure 3.2 Node a has two disjoint paths to node d, so its transmission range stays the

same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 3.3 Node a’s transmission range is increased to reach node e. . . . . . . . . . . 23

Figure 3.4 Node a has two disjoint paths to node f , so its transmission range stays the

same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 3.5 Node a has two disjoint paths to node g, so its transmission range stays the

same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 4.1 A Sample 2-Tiered WSN. . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Figure 4.2 Path information tables after supernode A transmits an INIT message. . . 32

Figure 4.3 Path information tables after node x transmits a PathIn f o message to node z. 33

Figure 4.4 Path information tables after node z transmits a PathIn f o message to node y. 34

Figure 4.5 Path information tables after supernode B transmits an INIT message. . . 35

Figure 4.6 Path information tables after node x transmits a PathIn f o message to node z. 36

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Figure 4.7 Path information tables after node z transmits PathIn f o message to nodes

x and y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Figure 4.8 Path information tables after node y transmits a PathIn f o message to node z. 38

Figure 4.9 Path information tables after node z transmits a PathIn f o message to node x. 39

Figure 4.10 Path information tables after supernode C transmits an INIT message. . . 40

Figure 4.11 Path information tables after node z transmits PathIn f o message to nodes

x and y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Figure 4.12 Disjoint paths and required neighbors for all sensor nodes after the path

information collection stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Figure 4.13 The final topology resulted after the application of the DPV algorithm. . . 44

Figure 4.14 Time Complexity Analysis of Finding Disjoint Paths. . . . . . . . . . . . . 45

Figure 4.15 Time Complexity Analysis of Path Information Collection Stage. . . . . . 46

Figure 5.1 Initial sample topology with 200 sensor and 10 supernodes. . . . . . . . . 52

Figure 5.2 Topology generated by DATC algorithm with h = 1. . . . . . . . . . . . . 53

Figure 5.3 Topology generated by DATC algorithm with h = 2. . . . . . . . . . . . . 54

Figure 5.4 Topology generated by our algorithm DPV. . . . . . . . . . . . . . . . . . 55

Figure 5.5 Optimum topology generated by GATC algorithm. . . . . . . . . . . . . . 56

Figure 5.6 Total Transmission Power for k = 2. . . . . . . . . . . . . . . . . . . . . . 57

Figure 5.7 Total Transmission Power for k = 3. . . . . . . . . . . . . . . . . . . . . . 58

Figure 5.8 Maximum Transmission Power for k = 2. . . . . . . . . . . . . . . . . . . 59

Figure 5.9 Maximum Transmission Power for k = 3. . . . . . . . . . . . . . . . . . . 60

Figure 5.10 Total Number of Links for k = 2. . . . . . . . . . . . . . . . . . . . . . . 61

Figure 5.11 Total Number of Links for k = 3. . . . . . . . . . . . . . . . . . . . . . . 62

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Figure 5.12 Number of Total Transmissions for k = 2. . . . . . . . . . . . . . . . . . . 64

Figure 5.13 Number of Total Transmissions for k = 3. . . . . . . . . . . . . . . . . . . 65

Figure 5.14 Number of Total Receptions for k = 2. . . . . . . . . . . . . . . . . . . . . 66

Figure 5.15 Number of Total Receptions for k = 3. . . . . . . . . . . . . . . . . . . . . 67

Figure 5.16 Total Transmission Power for k = 2 with PLR 0.1 and 0.2 . . . . . . . . . 69

Figure 5.17 Total Transmission Power for k = 2 with PLR 0.3 and 0.4 . . . . . . . . . 70

Figure 5.18 Total Number of Transmissions for k = 2 with PLR 0.1 and 0.2 . . . . . . 71

Figure 5.19 Total Number of Transmissions for k = 2 with PLR 0.3 and 0.4 . . . . . . 72

xvii

LIST OF ABBREVIATIONS

α − MOC −CDS α Minimum Routing Cost Connected Dominating Set

BAMP Biconnectivity Augmentation with MinMax Power

CA Collaborative Algorithm

CA-PCL Collaborative Algorithm with Probable Critical Link

CBTC Cone Based Topology Control

CDS Connected Dominating Set

CDSA Connected Dominating Set Augmentation

CMP Connected MinMax Power

CPU Central Processing Unit

DATC Fault Tolerant Distributed Anycast Topology Control

DGFT Distributed Geography-based Fault Tolerant Topology Control

DLSS Directed Local Spanning Subgraph

DPV Disjoint Path Vector

DRNG Directed Relative Neighborhood Graph

EECDS Energy Efficient Connected Dominating Set

FGSS Fault Tolerant Global Spanning Subgraph

FLSS Fault Tolerant Local Spanning Subgraph

FTTC Fault Tolerant Topology Control

GATC Fault Tolerant Global Anycast Topology Control

GG Gabriel Graph

k-ATC k-degree Anycast Topology Control

LILT Local Information Link State Topology

LINT Local Information No Topology

LMST Local Minimum Spanning Tree

MAC Medium Access Control

MCDS Minimum Connected Dominating Set

MST Minimum Spanning Tree

NAP Neighbor Addition Protocol

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PLR Packet Loss Ratio

RNG Relative Neighbor Graph

TCN Topology Control Neighbors

TTL Time To Live

WSAN Wireless Sensor and Actor Network

WSN Wireless Sensor Network

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CHAPTER 1

INTRODUCTION

Wireless sensor networks (WSNs) have been studied extensively in many aspects due to theirbroad range of potential monitoring and tracking applications including environmental obser-vation and habitat monitoring [2], [31], [15], fire detection [53], military applications [60],[26], [101], [80], health care solutions [49], [39], [3], [23], traffic tracking [10], [78], [83], smart buildings [58] and many other industrial applications [96], [36] , [41], [85]. WSNsare typically composed of tens or hundreds of tiny sensors that are capable of sensing somephenomena, processing and transmitting the data via a wireless channel. Sensor nodes col-laborate in a distributed and autonomous manner to accomplish a certain task usually in anenvironment without any infrastructure.

Sensor nodes in WSNs should be low cost and small in size in order to be used in hugeamounts in a real world application. This situation restricts the sensor nodes in many as-pects as they have limited power, short transmission range, relatively slow CPUs and a smallmemory. These limitations bring out many challenges unique to wireless sensor networks.

Power efficiency and fault tolerance are essential properties to have for WSNs in order to keepthe network functioning properly in case of energy depletion, hardware failures, communi-cation link errors, or adverse environmental conditions, events that are likely to occur quitefrequently in WSNs [21], [25], [11], [24], [19]. Topology control is one of the most importanttechniques used for reducing energy consumption and maintaining network connectivity [69].

In this thesis, we focus on fault-tolerant topology control in heterogeneous WSNs with a two-layered architecture where the lower layer consists of low-cost ordinary sensor nodes, withlimited battery power and short transmission range. The upper layer consists of supernodes,which have more power reserves and better processing and storage capabilities. Links be-tween supernodes have longer ranges and higher data rates; however, supernodes are fewer innumber due to their higher cost. Supernodes can also have some special abilities like actingagainst an event or a certain condition. This type of supernodes are called actors (or actua-tors), and sensor networks that contain actors are called wireless sensor and actor networks(WSAN). In WSANs, data gathered by sensors is forwarded to actors for performing the re-quired actions [29]. A heterogeneous WSN with supernodes are known to be more reliableand have longer network lifetime than the homogeneous counterparts without supernodes.Heterogeneity can triple the average delivery rate and provide a 5-fold increase in the net-work lifetime if supernodes are deployed carefully [59].

This thesis introduces a new algorithm called the Disjoint Path Vector (DPV) algorithm forconstructing a fault-tolerant topology to route data collected by sensor nodes to supernodes.

1

In WSNs, guaranteeing k-connectivity of the communication graph is fundamental to obtaina certain degree of fault tolerance [69]. The resulting topology is tolerant up to k − 1 nodefailures in the worst case. We propose a distributed algorithm, namely the DPV algorithm,for solving this problem in an efficient way in terms of total transmission power of the re-sulting topologies, maximum transmission power assigned to sensor nodes, and total numberof control message transmissions. Our simulations show that the DPV algorithm achieves a4-fold reduction in total transmission power and a 2-fold reduction in maximum transmissionpower compared to existing solutions. Under realistic packet loss scenarios our algorithmresults with 60% decrease in total transmission power. The power efficiency of our algorithmdirectly results from the novel approach that we apply while discovering the disjoint paths.This approach involves in storing full path information instead of just next node informationon the paths and provides a large search scope for discovering the best paths throughout thenetwork without the need of global network topology. The details of the proposed algorithmis described in Chapter 4.

The remainder of the thesis is organized as follows. In Chapter 2 we first give a brief overviewof key issues in wireless sensor networks (Section 2.1), then we continue by presenting a back-ground for our search which includes the following topics: Heterogeneous Wireless SensorNetworks (Section 2.2), Topology Control in Wireless Sensor Networks (Section 2.3) andFault Tolerance in Wireless Sensor Networks (Section 2.4). In Chapter 3 we present relatedapproaches related to our work in the literature. In Chapter 4 we describe our proposed algo-rithm in detail. Chapter 5 presents the evaluation results. We conclude the thesis with Section6.

2

CHAPTER 2

BACKGROUND

In this chapter we present a general background on wireless sensor networks, heterogeneity,topology control and fault tolerance in wireless sensor networks which constitute basics forour research.

2.1 Overview of Wireless Sensor Networks

In recent years, development of tiny and cheap sensors with processing capability and a wire-less communication subsystem enabled the wireless sensor networks (WSN) technology. Theaim of a WSN is to accomplish a monitoring or a tracking task by combining the local datasensed by the individual sensors. WSNs do not require an infrastructure and they can bedeployed in a random way on a geographical area and run autonomously without human in-tervention. Number of sensor nodes in a WSN can be in the order of tens, hundreds and eventhousands.

In homogeneous WSNs all the sensors in the network are identical whereas in a heterogeneousWSN some nodes are different than the others in some aspects like processing capabilities,transmitting range, storage and power capacity. Sensor nodes with higher capabilities areoften called supernodes. A gateway node can be considered as a supernode which directlytransmits the data collected from the sensor nodes to the base station. Heterogeneous WSNscan also include actor nodes (a special type of a supernode) which can show reaction whencertain events occur in the monitored region. This type of sensor networks are named aswireless sensor and actor networks(WSAN).

Sensor networks work in a data-centric manner and are usually lead by the queries startedfrom a base station. Sensor nodes which have data that satisfy the given conditions reply thequery by sending their sensed data. Usually data collected by the sensor nodes is sent to a basestation or a determined sink node which can be an actor or a supernode. The sensor nodes in asensor network typically use multihop communication instead of direct transmission in orderto save energy during the data transmission.

Key features and design challenges for wireless sensor networks can be summarized as fol-lows [13]:

• Sensor nodes are usually battery powered so WSN applications should be energy effi-cient in order to maximize the network lifetime.

3

• Sensor nodes are prone to failure and energy drain so WSN applications should be faulttolerant, that is, they should continue working in case of some node failures.

• Number of sensor nodes in a WSN application can be high, so the algorithms runningon WSNs should be scalable.

• Due to high number of sensors, getting the global topology information of the networkhas a high energy cost. Therefore algorithms running on sensor nodes should be dis-tributed and should be able to operate with local data.

• WSNs are usually deployed on infrastructureless geographical areas where manual in-tervention is not possible. For that reason sensor nodes should be self organizing andautonomously operating in order to achieve their mission.

In addition to the key features and challenges mentioned above there are also many specialrequirements for different types of WSN applications including quality of service (QoS), realtime communication, time synchronization among the sensor nodes, localization, coverageand connectivity requirements, secure communication, in network query evaluation, data ag-gregation, special protocols for routing and handling mobility.

Mainly five different types of WSNs exist [36]:

1. Terrestrial WSN: Consists of high number low-cost sensor nodes. Reliable commu-nication among the densely deployed sensor nodes are important. Terrestrial WSNscan both be deployed in a random way or according to a deployment plan. Randomdeployment can be done by throwing the sensors from an airplane on a geographicalarea.

2. Underground WSN: In order to monitor the underground conditions sensor nodes areburied into the soil or put in cave, mine or so on. Nodes above the ground are locatedto gather the data from the sensor nodes and relay it to the base station. Sensor nodesare more expensive in underground WSNs according to terrestrial WSNs because theyshould be durable to harsh underground conditions and require specialized equipmentsin order to communicate under the high attenuation and signal loss. In addition, avery carefully planned deployment of sensor nodes is required since the sensors areexpensive and redeployment is not an option.

3. Underwater WSN: Number of sensors in an underwater WSN is much fewer than aterrestrial WSN both because they are more expensive and they use acoustic waves forcommunication which is not suitable for dense deployment. Data from the sensor nodesare collected by the autonomous underwater vehicles. Low bandwidth and high latencyare challenging problems for this type of WSNs.

4. Multi-media WSN: Consists of sensor nodes equipped with camera and microphone.They are deployed according to a plan in order to ensure the coverage of the monitoredarea. Multi-media WSNs require high bandwidth, quality of service and high energyconsumption.

5. Mobile WSN: Consists of sensor nodes with capability of moving in order to reposi-tion themselves in the network topology. Mobile nodes can move to area of events andcommunicate with other nodes when they are in communication range. They require

4

dynamic routing protocols in contrast to static sensor networks. Localization, naviga-tion and controlling the coverage and connectivity are the main challenges for a mobileWSN.

Here are some application areas of wireless sensor networks and examples among many others

• Military Applications: Border protection, battlefield surveillance, soldier detection andtracking, anti-submarine warfare, chemical/biological vapor detection and soldier wear-able sensors [47], [60], [26], [101], [80].

• Environmental Monitoring: Forest fire detection, habitat monitoring, animal tracking,pollution detection, volcano eruption monitoring [53], [2], [31], [15].

• Health care Applications: Vital sign monitoring in hospitals, monitoring aged people athome, large-scale in-field medical studies [49], [39], [3], [23].

• Industrial Applications: Building and factory automation, industrial equipment mon-itoring, process monitoring and control, underground mine monitoring, offshore oilstation monitoring [96], [36] , [41], [85], [56].

• Traffic Monitoring: Traffic load prediction, vehicle routing and tracking, dynamic trafficsignaling, intelligent transportation systems, logistics [52], [92], [10], [78], [83] .

• Disaster Relief and Rescue: Detection of survivors after an earthquake [79], [66], [17].

• Smart Buildings: Smart home automation, energy efficient buildings [8], [30].

2.2 Heterogeneous Wireless Sensor Networks

Heterogeneous wireless sensor networks consist of nodes with different capabilities. Nodesmay differ in sensing capabilities, transmitting range, processing power, energy capacity,amount of storage and so on. Nodes with superior capabilities according to normal nodesare called supernodes.

Supernodes can have different roles according to the applications. Some supernodes justoverlay the data collected from the sensor nodes to a base station. In this scenario a supernodeis a gateway node. Supernodes can also make additional processing on the collected databefore sending it to a base station. A supernode can apply some filters or can make dataaggregation to decrease the amount of data to be transmitted which also decreases the energyconsumption.

Supernodes can also have some special abilities like acting against an event or a certain con-dition. This type of supernodes called as actors (or actuators) and sensor networks that con-tain actors are called wireless sensor and actor networks (WSAN). WSANs usually have atwo-layer architecture where the lower level is composed of low cost sensor nodes and theupper layer consists of resource-rich actor nodes which take decisions and perform appropri-ate actions [29]. In WSANs, there are usually two types of wireless communication links:actor-actor and sensor-actor links [35]. The links between sensors and actors are assumedto be less reliable [40], hence there are several methods proposed for maintaining reliable

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sensor-actor connectivity [35], [40], [81]. The methods of [40] and [81], however, do not em-ploy k-connectivity between sensors and actors and thus they do not guarantee fault-tolerancein case of k − 1 node failures. Although [35] addresses the k-actor connectivity problem, itdoes not consider the energy efficiency of the resulting topologies. Our approach differs fromthese works by maintaining k-connectivity and addressing power efficiency at the same time.

Another special type of heterogeneity arises when the sensor nodes in a WSN have the abilityof tuning the transmission power. In such a network each sensor node adjusts its transmissionpower according to a topology control algorithm which generates a topology with unequaltransmission ranges. This approach is useful for energy conservation but arising unidirectionallinks should be handled carefully.

A heterogeneous WSN with supernodes are known to be more reliable and have longer net-work lifetime than the homogeneous counterparts without supernodes. Yarvis et al. [59]reported that heterogeneity can triple the average delivery rate and provide a 5-fold increasein the network lifetime if supernodes are deployed carefully. This is apparent since ordinarysensor nodes will not be required to relay the sensed data all the way to the base station, in-stead data will be sent to a near supernode which has larger energy resources than the ordinarysensor nodes in the network.

In this work we mainly focus on heterogeneous wireless sensor networks with two layeredarchitecture as defined in [51]. There are two types of nodes in our target WSN. In the lowerlayer we have low cost ordinary sensor nodes with restrictions like limited battery power, shorttransmission range, small storage, low data rate and low duty cycle. The upper layer consistsof supernodes which have more power reserves, better processing and storage capabilities.Links between supernodes have longer ranges and higher data rates. Number of supernodes isfewer than the ordinary sensors due to their higher cost. We do not have special requirementson the supernodes, they can be gateways, in network query evaluators, data aggregators oractors. All supernodes in the network are assumed to be identical so delivering the senseddata to any of the supernodes is sufficient. Supernode - supernode and supernode - basestation communication is out of the scope of this work.

2.3 Topology Control in Wireless Sensor Networks

In wireless sensor networks, most of the time, deployment is not done manually and so net-work topology cannot be known beforehand. Network topology is constructed autonomouslyby the sensors after the deployment to the application area. Hence a topology control mech-anism is needed to build and maintain the network topology. In addition, topology in WSNsis subject to change for several reasons including communication link breaks, nodes runningout of power, and mobility. In order to keep the network connected as long as possible andoptimize the network lifetime and throughput, topology control mechanisms are essential forWSNs.

Topology control is defined as controlling the neighbor set of nodes in a WSN by adjustingtransmission range and/or selecting specific nodes to forward the messages [98]. Topologycontrol approaches can be divided into two main categories, namely, homogeneous and non-homogeneous [69]. In homogeneous approaches transmission range of all sensors are thesame whereas in nonhomogeneous approaches nodes can have different transmission ranges.

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We can also distinguish the proposed topology control approaches based on the type of thenetwork topology they address. Most approaches address flat topologies whereas only a fewaddress heterogeneous topologies where the network consists of different types of nodes. Ourproposed approach is in the latter category and is different from most of the approaches in thisway.

There are many topology control mechanisms in the literature and they can be classified ac-cording to the techniques they use. Many topology control methods [54], [46], [62], [51],[61], [64], [77], [50], [16] are built on the transmit power adjustment technique which de-pends on the sensors that can control their transmit power. Some algorithms [6], [95], [76],[9], [97] use sleep scheduling which aims to decrease energy consumption while nodes arein idle state. Others use geometrical structures, location and direction information, clusteringapproaches and also combinations of the mentioned techniques [100], [67], [65], [93]. Santi[69] says that approaches that do not modify the transmit power of the nodes cannot be clas-sified as topology control mechanisms but we adopt a more inclusive definition of topologycontrol given by Wang [98] that is controlling set of neighbors by adjusting transmission rangeand/or selecting specific nodes to forward the messages. Selection of the (logical) neighborsdepends on the topology control approach which is designed to meet the requirements for acertain scenario.

Clustering can also be considered as another way of topology control, where the aim is toorganize the network into a connected hierarchy for the purpose of balancing load amongthe nodes and prolonging the network lifetime [68]. Hierarchical clustering techniques [74],[43] select cluster heads depending on various criteria and creates a layered architecture.However, these techniques start with a flat topology and end up with a layered one. On theother hand, we start with a layered architecture from the beginning, where the supernodes arealready given. Instead of building clusters, we focus on maintaining fault-tolerant connectivitybetween sensor nodes and supernodes.

We give a taxonomy of existing topology control approaches below.

Santi [69] groups the topology control mechanisms as follows:

• Homogeneous: Nodes use same transmitting range. The aim is to find a minimumrange value that satisfies a certain property.

• Nonhomogeneous: Nodes can have different transmitting range less than a maximumvalue.

– Location based: Exact positions of the sensor nodes are known.

∗ Range assignment and variants: Location information is used by a centralizedauthority to assign transmission ranges for each node.

∗ Energy-efficient communication: Location information is used in a localizedmanner to establish a energy efficient topology.

– Direction based: Exact node locations are not known but nodes can estimate rela-tive directions of their neighbors.

– Neighbor based: Nodes can distinguish their neighbors according to some mea-sure like distance.

Li et al. [55] gives a taxonomy of topology control problems as follows:

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• Sensor Coverage Topology: Focuses on the maximization of sensor coverage area whileusing less power. Approaches exist targeting the following types of sensor networks:

– Static Networks

– Mobile Networks

– Hybrid Networks

• Sensor Connectivity Topology: Aims to keep the network functioning in an energyefficient manner while preserving the network connectivity.

– Power control mechanisms: Uses power adjustment techniques to obtain a con-nected and energy efficient network topology.

– Power Management Mechanisms: Uses wake/sleep schedules to conserve energyby sending the redundant nodes to sleep.

Energy efficiency is critical for wireless sensor networks because they are composed of energy-constrained sensor nodes. Topology control mechanisms can help WSNs save energy usingpower adjustment techniques and wake/sleep schedules. According to Zhang et al. besidepower control and sleep scheduling, an energy-efficient topology control algorithm have to beaware of traffic load and run in conjunction with routing protocol [94].

Having presented general taxonomies for topology control problems and mechanisms, wenow give a brief background about geometric structures frequently used in topology controlalgorithms.

2.3.1 Geometrical Structures

2.3.1.1 RNG and GG

The relative neighbor graph (RNG) [38] consists of all edges uv ∈ E such that there is novertex w ∈ V with edges uw and wv ∈ E satisfying ‖uw‖ < ‖uv‖ and ‖wv‖ < ‖uv‖. Thedefinition of RNG is shown in Figure 2.1(a). The brute-force algorithm for creating RNG ofa graph with N nodes takes O(N3) time [12]. More efficient methods also exist for computingRNG. For instance, Supowit’s cone based search method finds RNG of a graph in O(NlogN)[42].

Gabriel graph (GG) [44] contains an edge uv if and only if there is no other vertex w ∈ V inthe disk with diameter uv such that uw and wv ∈ E. The definition of GG is shown in Figure2.1(b).

If the initial unidirectional graph G is connected, the constructed RNG and GG graphs arealso connected which is important for wireless sensor networks. These structures can alsobe built in a localized manner by using only one hope neighbor information which is also adesirable feature for WSNs.

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2.3.1.2 Minimum Spanning Tree

Minimum spanning trees (MST) are frequently used in topology control algorithms since theyconsist of the edges that keep the graph in one connected component, where the total cost ofthe edges is minimum. The most known algorithms for computing the MST of a graph areKruskal’s [37] and Prim’s [73] algorithms. These two algorithms use greedy approach andrequire global network topology information.

Kruskal’s algorithm grows a forest by adding a safe edge with the least weight at each step un-til all nodes in the graph get connected. The computational cost of the algorithm is O(ElogE)where E is the number of edges in the graph [82].

Unlike Kruskal’s algorithm, Prim’s algorithm grows a single tree instead of a forest. It startsfrom an arbitrary node and at each step it adds the least cost edge that connects the currenttree to an uncovered node in the graph. The computational cost of Prim’s algorithm is O(E +

NlogN) where N is the number of nodes in the graph [82].

In wireless sensor networks, most of the time, global network topology is not known to everysensor node and it is also expensive to acquire that information. For that reason, distributedalgorithms using local information are more practical for real WSN applications. For instanceLocal Minimum Spanning Tree (LMST) [65] protocol and LMSTk [93] algorithm are intro-duced to build a MST-like network topology using only local information in a distributedmanner. Li and Hou [61] introduce fault tolerant topology control algorithms based on MST,namely Fault Tolerant Global Spanning Subgraph (FGSS) and Fault Tolerant Local SpanningSubgraph (FLSS) where the former is centralized and the latter is localized.

2.3.1.3 Delaunay Triangulation

Triangulation of set of vertices in V such that no triangle’s circumcircle contain any othervertices, is a Delaunay Triangulation. (Assuming there are no four co-circular vertices inV). This structure is not very useful for wireless sensor networks since its construction maycause a high communication overhead because the a triangle can be much larger than thetransmission ranges of the sensor nodes which leads to need for global network information.The definition of RNG is shown in Figure 2.1(c).

2.3.1.4 Bounded Degree Spanners

Since MAC-level contention and interference are reduced when node degrees are small, nodedegree bounded topologies are desirable for wireless sensor networks.

Suppose a node u divides the plane into k equal sized cones with rays originating from u. Yaograph [4] is constructed by finding the shortest edges from u to v in each cone and adding thedirectional link uv for corresponding edge. Yao graph formation is shown in Figure 2.2. Ifthe link vu is added instead of the link uv, the resulting graph is the reverse of the Yao graph.If in each cone, the edge that has the shortest projection on the angular bisector of the cone isadded, the resulting graph is called θ − graph.

In a Yao graph, a node u has a bounded out-degree but it can have unbounded in-degree values

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Figure 2.1: RNG, GG and Delaunay Triangulation.

Figure 2.2: Yao Graph Formation.

which may result large communication overhead for node u.

There are also proposed structures for topology control which combine geometric structuresand bounded degree spanners. For instance [88] Song et al. proposed a new structure calledSYaoGG by applying the ordered Yao structures onto a Gabriel graph. According to thisstructure, it is guaranteed that there is at most one neighbor node in each of the k equal sizedcones of the Yao structure. In a more recent work [87] Song et al. proposed an improvedmethod to further reduce the contention by selecting fewer neighbors for communication.They called the final topology generated by this method as SθGG for power efficient unicasttopology. The basic idea of this approach is to remove some links from the underlying Gabrielgraph without breaking the power spanner property. In the same work, they also proposedunified power efficient topology for unicast and broadcast called LSθGG. The importance ofthis work is that it produces a power spanner, bounded node degree, planar topology with lowaverage interference with a localized topology control algorithm.

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2.3.1.5 Virtual Backbones

Beside the mentioned flat geometrical structures, there are also hierarchical structures thatcan be used to control wireless sensor network topologies. In hierarchical topologies, a subsetof sensor nodes that behave as gateway or backbone nodes relay packets only. Other sensornodes send their collected data to these backbone nodes.

Connected dominating sets are often used to construct virtual backbone structures. A domi-nating set for a graph G = (V, E) is a subset D of V such that every vertex not in D is adjacentto at least one vertex in D by some edge. If D induces a connected subgraph, then it is aconnected dominating set. A connected dominating set is said to be minimum (MCDS) if itincludes the minimum number of vertices. An MCDS is a useful structure because it providescommunication by only using a small subset of nodes in the network. However, problemof finding a MCDS for an arbitrary network is NP-complete [84], so we need to use heuris-tics and approximation algorithms. The basic idea behind these algorithms is to construct adominating set first and then add extra nodes in order to obtain a connected dominating set.Another approach is building a redundant CDS and then removing nodes to get a smaller sizedCDS. Some of these algorithms can be found in the following works [75], [86], [14], [57],[33] and [34].

Wightman et al. [70] propose a CDS based topology control algorithm called the A3 whichselects the CDS tree nodes based on the signal strength and remaining energy. This algorithmresults a sub-optimal CDS with relatively longer edge lengths which causes long distancecommunications. Yuanyuan et. al [102] propose a topology control algorithm called theEnergy Efficient CDS (EECDS) which constructs a sub-optimal CDS by first selecting clusterheads and than gateways. Cluster-heads control uniform distribution of energy resourcesamong the network.

Ding et al. [45] introduces a special kind of CDS which is called α Minimum Routing CostConnected Dominating Set α − MOC − CDS in order to achieve efficient broadcasting androuting in wireless networks. The difference between an α−MOC −CDS and a conventionalCDS is that, in α−MOC−CDS for any pair of nodes, there is at least one shortest path betweenall pairs where the intermediate nodes on the shortest paths all included in α − MOC −CDS .Therefore it is still possible to send packages over shortest paths as in the original network. Inthis work, authors also define another dominating set called α−2hop−DS and they prove thatthey are equivalent with each other. They propose a heuristic localized algorithm to constructan α − 2hop − DS .

As the authors of [20] and [99] reported, CDS-based topology control algorithms have rel-atively lower fault tolerance to random link and node failures because in a CDS, each linkserves as a bridge and in case of the failure of these links, some nodes may become discon-nected. In order to increase the reliability of the CDS structure, they proposed two algorithms,namely, Connected Dominating Set Augmentation (CDSA) and k-connected m-dominatingset (k,mCDS) to build a k-connected CDS structure.

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2.4 Fault Tolerance in Wireless Sensor Networks

Fault tolerance can be defined as the ability of a system to keep functioning at a desiredlevel in case of faults which occur frequently in many wireless sensor networks due to errorprone nature of sensor nodes. There are various factors which cause faults in sensor nodeslike energy depletion, hardware failure, communication link errors, malicious attack and soon [25]. In addition, links are also failure prone which may fail permanently or temporarilywhen blocked by external objects or environmental conditions. Congestion may also leadto faults by causing packet loss due to simultaneous transmission of larger number of sensornodes [48]. Multihop communication multiplies the faults that can arise in WSN applications.Therefore fault tolerance is an essential requirement for most wireless sensor applications andthere are many works addressing this problem in the literature.

Fault tolerance can be addressed at different layers including hardware layer, software layer,network communication layer and application layer. Our primary focus will be on applicationlayer solutions like finding multiple node-disjoint or braided paths, having a certain degree ofconnectivity of sensor nodes to the sinks, monitoring energy levels of the sensor nodes andmaintaining the most reliable paths. Paradis et al [48] lists the reasons why faults in sensornetworks cannot be handled in the same way as in traditional wired or wireless networks asfollows:

1. Energy consumption is not a constraint for constantly powered wired or rechargeablead hoc devices.

2. Point to point reliability is important for traditional network protocols, but reliable pathsfrom data source to sinks are more important in WSNs.

3. In WSNs node failures occur much more frequently than the traditional wired or ad hocnetworks.

4. MAC protocols in WSNs are not sophisticated as in traditional wireless networks.

For the reasons listed above, requirement for new fault tolerant methods has become clear andseveral techniques are developed for wireless sensor network applications.

Fault tolerant techniques can be categorized into five main groups [5]:

• Fault prevention: Includes ensuring network connectivity and coverage at the designstage, monitoring network status and taking reactive actions when necessary and main-taining redundant links and nodes.

• Fault detection: Largely depends on the type of the application and type of faults. Mainindication of faults are packet loss (decrease in packet delivery rate), interruption, delayin network traffic.

• Fault isolation and identification: Diagnoses and determines the real causes for detectedalarms in the network in order to take the right actions.

• Fault recovery: Faults can be recovered within the sensor network or at the sink afterthe data collection and analysis. Fault recovery within the network is more appropriatefor WSN applications since it is costly to forward the data to the sink.

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Replication and redundancy of components which are prone to failure is most commonlyused method for fault prevention and recovery [25]. For instance if some nodes have prob-lems and fail to sense the environment, redundant nodes in the vicinity can still provide data.Keeping redundant links or multiple paths also provides a fault tolerance when some of thecommunication links are broken due to node failures or communication problems.

In order to improve reliability and prolong the network lifetime of sensor networks, a twotiered network architecture can be used instead of a flat topology. This method introducesan upper level consisting of powerful relay nodes on top of ordinary sensor nodes. Thesepowerful nodes gather information from sensors and send them directly to base station or viaother relay nodes. Hence, sensor nodes do not consume energy for data relaying as muchas in the case of flat topology because they send the data to a relay node which is mostprobably closer than the base station. In order to have a fault tolerant topology each sensor isassigned to more than one relay node, so a sensor node can switch to other relay nodes whencommunication with the current relay node is lost. Powerful nodes can also process the datagathered by the sensors before sending them to base station which decreases the size of thedata transmitted and the energy consumption for transmission.

Relay node placement is a common technique to achieve a certain degree of fault tolerancein two tiered WSNs. There are many works addressing relay node placement in the literature[91], [18], [1], [32], [89] and [90]. The objective is to locate the minimum number of relaynodes to a region with a set of sensors randomly deployed, in order to ensure that each sensornode is covered by at least one relay node and the resulting network topology is k-connected.

Although relay node placement seems to be useful to achieve fault tolerance, it is not verypractical in some aspects. First of all in most scenarios since the sensor nodes are deployedto remote regions it is not feasible to make a manual deployment of relay nodes. Secondly,proposed methods to determine the locations of the relay nodes to be deployed require globalnetwork information which is not suitable for real applications. Besides, WSNs have a dy-namic network topology due to reasons like energy depletion and link errors so node place-ment needs be repeated to keep network connected and fault tolerant which is not practicalin real WSN applications. Therefore a topology control approach should be used to constructand maintain the fault tolerance property of the network.

As stated by Liu et al [25], most of the existing works about fault tolerant topology controlaims to obtain k-vertex connectivity between any two sensor nodes in the network. How-ever for WSN applications, it is more important to have fault tolerant paths from sensors tosinks. There are works addressing this problem which make use of power adjustment andgeometrical structures which will be discussed in Chapter 3 in detail.

Data gathering and aggregation of the sensed data is on the core of WSN applications. Gen-eral approach used is to construct a spanning tree connecting all the nodes in the network.However tree structures are not fault tolerant since a subtree becomes disconnected if anynode or communication failure occurs. Therefore we require extended geometric structureswhich have redundant links or multiple paths toward sinks in order to achieve fault tolerance.

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CHAPTER 3

RELATED WORK

In this chapter we will give a brief overview of the prominent recent work addressing topologycontrol in wireless sensor networks which is related to our research topic. We will grant moreattention on the solutions that also consider the fault tolerance and heterogeneity.

Chen et al [95] proposes a fault tolerant topology control approach (FTTC) which aims toachieve a certain degree of vertex connectivity. In this approach, each node first runs SPAN [6]protocol to construct a connected dominating set (CDS). All nodes in CDS mark themselves.Then each node in the CDS adds necessary nodes and marks them until reaching to desiredlocal vertex connectivity. All marked nodes stay in wakeup state and unmarked nodes go tosleep state. In order to balance energy consumption, a rotation process is included in thisapproach. Authors also prove that ensuring local vertex connectivity degree also guaranteesthe global vertex connectivity degree. They perform simulations with different node selectioncriteria including power based, connection degree based, cut bridge based and report that cutbridge based selection is better for extending the network lifetime. They do not provide acomparison with previous approaches. This work focuses on the flat topologies, whereas ourwork focuses on the two layered heterogeneous topologies.

Another CDS based reliable topology control protocol for wireless sensor networks called thePoly is proposed by Qureshi et al. [27]. The topology construction algorithm in this protocolis based on the idea of polygons. Subsets of the nodes in the network are arranged so that theyform a closed path which provides a reliable topology because there is an alternative path tosink. It is also energy efficient because the nodes that are not in the set of nodes comprising apolygon can go to sleep mode. In addition this protocol does not need the location informationof the nodes. Qureshi et al. compare their protocol with existing protocols which are alsobased on CDS, namely, Energy Efficient CDS (EECDS) [102], CDS-Rule K [34] and A3 [70].They report that Poly is 120% more reliable than these protocols. However, Poly protocol doesnot fit to our problem, since it does not consider the k-connectivity of each node to sinks. Apolygon structure can only provide 2-connectivity for the nodes in the polygon structure. Thenodes that are not in a polygon structure are guaranteed to be 2-connected. In addition thisprotocol is not developed for layered heterogeneous network topologies.

Borbash et al [77] presents an algorithm for topology control for multihop wireless networksbased on the relative neighborhood graph (RNG). Authors introduce a distributed algorithmto compute RNG by using local information and directional information of incoming signals.Each node incrementally adjusts its transmission power to obtain the desired network topol-ogy. They also perform simulations to compare RNG with minimum spanning tree MST andminimum radius graph (minR) with respect to transmission radius, hop diameter, node degree

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and biconnectivity. They report that transmission radius of RNG approaches to that of MSTwhich has the minimum transmission radius as the number of nodes increases. Simulationsalso show that hop diameter of RNG is closer to that of minR which achieves the minimum.In addition, RNG and MST node degrees are bounded by a small constant where node degreeof minR increases linearly as the number of nodes increases. They find out that approximately%90 of the nodes are in the same biconnected component where minR is always biconnected.This algorithm is for flat topologies and also does not consider the fault tolerance.

Li et al [65] proposes a distributed topology control algorithm based on Minimum SpanningTree (MST), called Local Minimum Spanning Tree (LMST) for wireless multi-hop networks.According to LMST algorithm each node calculates its local MST by using Prim’s algorithmby using the local information gathered from the neighbors reachable with maximum trans-mission power. In the topology construction phase, a node u adds node v to its neighbor listif and only if node v is in u’s local MST and one hop away from u. After the determinationof neighbor lists each node adjusts its transmission power that will be sufficient to reach itsneighbors in the resulting topology. Bidirectionality of the links is achieved either by deletingall unidirectional links or forcing the unidirectional links to become bidirectional. Authorsprove that resulting topology preserves the network connectivity and degree of any node isbounded by 6. Simulation results show that LMST has a small average node degree whichhelps reducing MAC-level contention and small transmission radius which means a smalltransmission power is required to keep the network connected. LMST algorithm is devel-oped for homogeneous flat network topologies whereas our work focuses on the two-layeredheterogeneous topologies.

Wang et al [50] proposes an algorithm called Distributed Geography-based Fault Toleranttopology control algorithm (DGFT) which produces a bidirectional and strongly connectedtopology. In this approach deployment area is divided into a set of centric circles with thesame center O resulting rings with equal width ω. Each node knows its location and the ringit belongs to. By exchanging HELLO messages each node calculates its reachable neighborset, and its neighbors in the inner and outer rings. Topology construction is performed byselecting neighbors from the inner rings according to certain initialized weights. Nodes ad-just their power to select the logical neighbors. Authors show that average node degrees ofthe topologies generated by DGFT are larger than that of Dist_RNG [77] and LMST [65]algorithms. They also report that DGFT is more robust against random node failures thanDist_RNG and LMST according to the network fragmentation criterion. Although this workconsiders the fault tolerance, it is for homogeneous flat network topologies where our solutionaddresses the two-layered heterogeneous topologies.

Blough et al [16] proposes a distributed, localized and asynchronous topology control mech-anism called k-NEIGH which aims to keep the number of neighbors of every node equalto or slightly below a specific value k. k-NEIGH protocol makes use of power adjustmenttechnique after the neighbor determination step where each node in the network selects thek nearest neighbors. Neighbor lists are exchanged between one hop neighbors to find outthe bidirectional links. Unidirectional links are discarded in the final topology. Transmissionpower is set to a value which is needed to transmit to the farthest neighbor for each node.k-NEIGH also includes an optional pruning procedure which investigates if there is a morepower efficient path which includes an intermediate node than an existing direct link for allneighbors of a node. If such an intermediate node exists, direct edge is replaced with theedge between the current node and the intermediate node. After this pruning stage, eachnode adjusts its transmission power according to the resulting pruned neighbor list. Authors

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run simulations to find the preferred values for k for different number of nodes which resulta connected network with probability > 0.95. They also compare energy efficiency of thetopology generated by k-NEIGH with the topology generated by CBTC [72] protocol. Sim-ulation results show that k-NEIGH performs significantly better than CBCT with respect toenergy cost. This solution considers the connectivity between sensor nodes in a flat homoge-neous network topology whereas our work targets k-connectivity between sensor nodes andsupernodes which constitute a two-layered heterogeneous network topology.

Ramanathan et al [71] formulates the topology control of multihop wireless networks as a con-strained optimization problem where the objective is to minimize the transmission power sub-ject to keeping the network connected. Authors define the optimization problems ConnectedMinMax Power (CMP) and Biconnectivity Augmentation with MinMax Power (BAMP) tofind a per-node minimal assignment of transmit powers for connectivity and biconnectivityrespectively. They present two centralized algorithms CONNECT and BICONN giving op-timal solutions for the problems CMP and BAMP for static networks. They also proposedistributed heuristic methods for mobile networks namely Local Information No Topology(LINT) and Local Information Link State Topology (LILT). LINT tries to keep the number ofactive neighbors around specified threshold by dynamically adjusting the transmission power.When the number of neighbors becomes less than the threshold value, it increases the trans-mission power and when the number of neighbors becomes greater than the threshold value,it decreases the transmission power. LINT does not consider the network connectivity whileadjusting the transmission power. In order to prevent the disconnectivity, LILT algorithm isproposed. LILT makes use of the link-state information to recognize and repair the networkpartitions. Neighbor Addition Protocol (NAP) is triggered whenever an event driven or peri-odic link-state update arrives. NAP sets the transmission power of the node to maximum inorder to establish the connectivity when the network becomes disconnected.

In [71] authors make simulations to compare the throughput, delay, average and maximumtransmit power for the topologies generated by CONNECT and BICONN for static networks,LINT and LILT for mobile networks, with topologies that have no topology control. Resultsshow that topologies generated by BICONN provide more throughput but consume morepower than CONNECT. LINT and LILT give similar results on throughput which are quitebetter than no topology control in general. However in dense networks, LILT performs worsethan no topology control. CONNECT and BICONN have a little importance for use in realapplications due to requirement of global topology information. However, topologies gen-erated by them can be used as a reference since they give the optimal solution for per-nodeminimality of transmission power. Although LINT and LILT are designed for mobile net-works, they can also be used in dynamic environments as in sensor networks for topologycontrol. The algorithms in [71] focuses on the connectivity between sensor nodes and do notdirectly apply for two-layered heterogeneous sensor networks.

As seen in [71] trying to maintain a fixed node degree can cause partitioning of the networkdue to increasing or decreasing the transmission range of the nodes without collaboration.Srivastava et al [22] focuses on this problem and identifies the cases that lead to disconnectednetwork and isolated nodes when a fixed node degree approach is applied. They propose twodistributed algorithms to improve the connectivity of the fixed node topologies by maintain-ing critical links when necessary. The proposed algorithms use one hop local informationand positions of the nodes and combine unidirectional link information in topology controldecisions. We will briefly discuss the proposed algorithms, namely Collaborative Algorithm(CA) and Collaborative Algorithm with Probable Critical Link (CA-PCL).

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The main objective of the CA algorithm is to identify the unidirectional links which may arisewhen a fixed node local topology control approach is used. Having identified the unidirec-tional links, CA algorithm adds extra links to the local topology graph to convert the unidi-rectional links to bidirectional ones. In CA algorithm each node starts by running Construct-TCN() procedure to select its topology control neighbors (TCN). First, each node transmita HELLO message which includes the id of the transmitting node. Any node receiving aHELLO message adds the id of the node in the message to its neighbor list (Ni). Nodes inlist Ni is sorted according to increasing distance from the node i. After the identification ofthe neighbors in the vicinity, each node adds the first k nodes to its TCN list to obtain a fixednode topology. Notice that TCN list contains the unidirectional neighbors. In order to find thebidirectional neighbors, Bidirectional-TCN() procedure is run by each node. In Bidirectional-TCN() each node transmits its TCN list at maximum power. Any node receiving a TCN list,calculates the list of bidirectional neighbors by comparing with its local unidirectional neigh-bor list(TCN). Finally, Convert-TCN() procedure is run by each node which iterates the TCNlist of the nodes in list Ni (list of all neighbors) and adds the nodes to its bidirectional nodelist (BTCN) which have node i in their TCN lists.

Although the CA algorithm improves the connectivity of the network, in some cases it isstill possible that the network stays disconnected. This situation occurs when all the nodessatisfy the desired node degree and they form clusters which are not connected to each other.In order to solve this problem Srivastava et al [22] propose the CA-PCL algorithm whichidentifies the probable critical links that may be essential for the network connectivity. InCritical-TCN() procedure, critical links are found locally by using maximum transmissionpower. This is achieved by first detecting the articulation points whose removal makes thenetwork disconnected. A link connecting to an articulation point is considered as a probablecritical link and added to the TCN of the link that runs the Critical-TCN() procedure. Anarticulation point is found by Lune method which is also used to construct the RNG graphs.If a node exists in the Lune(i, j) of the nodes i and j, then the link between i and j is notconsidered as a critical link because there exists an alternative path between these nodes. Ifthere is no node in Lune(i, j), it means that there may not be other paths that connect thesetwo nodes, so it is marked as a probable critical link. Since this search is made in the localneighborhood, resulting links may not be the global critical links and therefore they are calledas probable critical links. For that reason we should also be aware that inclusion of thesecritical links can cause extra link redundancy.

The simulation results show that the connectivity that CA and CA-PCL provide is significantlyhigher than that of LINT. The transmission power required for the topologies generated by CAis also lower than that of LINT but CA-PCL has an average maximum transmission powerthat is greater than LINT. This is due to the Critical-TCN() procedure. In addition, simulationresults also show that topologies generated by CA-PCL is more tolerant to node failures thanthe RNG topologies distributedly generated by Dist-RNG [12] algorithm. The algorithms in[22] are not developed for the heterogeneous two-layered network architectures.

Li and Hou [61],[64] propose two algorithms addressing the k-connectivity problem with theobjective of minimizing the maximum transmission radius among all nodes in the network.The first algorithm they introduced is called Fault Tolerant Global Spanning Subgraph (FGSS)which is a centralized greedy algorithm. It is aimed to build k-connected spanning subgraphsbased on the well known Kruskal’s algorithm. Since FGSS is a centralized algorithm thatrequires the global knowledge of network, which is difficult to collect and distribute throughthe network, they also proposed a localized algorithm called Fault Tolerant Local Spanning

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Subgraph (FLSS). In this algorithm, each node selects its own set of neighbors and finallyadjusts its transmission power based on the local information. They proved that FLSS min-imizes the maximum transmission power of nodes among all strictly localized algorithms.The difference between the problem focused in this work and our work is that we try to min-imize the total transmission power of the nodes whereas Li and Hou minimize the maximumtransmission power. In addition our focus is on the 2-tiered heterogeneous sensor networkwhereas they primarily focus on the flat homogeneous wireless ad hoc networks. Their ob-jective is to keep k-connectivity between any two nodes but we are concerned with providingk-connectivity from each sensor to the set of supernodes.

For multi-hop wireless networks with nonuniform transmission ranges, Li et al. [63] proposetwo algorithms, namely, Directed Relative Neighborhood Graph (DRNG) and Directed LocalSpanning Subgraph (DLSS). Both algorithms use locally collected information to constructthe final network topology. These algorithms have three phases, namely, information collec-tion, topology construction and bidirectional link construction. The last phase is optional thatis used only when a bidirectional topology is required. In the information collection stageeach node collects the information of its visible neighborhood. This is achieved periodicallybroadcasting Hello messages that include the id, the maximal transmission power and theposition of the node. In the topology construction phase the DRNG algorithm constructsa directed relative neighborhood graph whereas the DLSS builds a directed local spanningsubgraph. Since each node determines its neighbors independently, some links in the finaltopology may be uni-directional. So, if required, the optional third phase is run to obtain abidirectional topology either by applying link addition or removal methods. The simulationresults show that the DLSS performs better than the DRNG in terms of average radius, aver-age node degree and average link length. The notion of heterogeneity in Li et al.’s work isdifferent than ours because we focus on a two-layer topology where layers are composed ofdifferent type of nodes. For that reason, the problem they address is different than ours andthe solutions they provide cannot be directly applied to our problem. In addition, they do notconsider the fault tolerance of the resulting topologies.

A prominent work on fault-tolerant topology control for wireless multi-hop networks is pro-posed by Saha et al [28]. Their algorithm is a distributed one assigning the nodes approxi-mately minimum power using locally collected data and it results a network topology whereany two nodes in the global network is connected by k-vertex disjoint paths provided theinitial graph is k-connected. The algorithm has three phases, namely, information collectionand finding the vicinity topology, construction of the minimum-power vicinity topology andfinally transmission power assignment. In the first phase the vicinity information is collectedvia Hello messages. The critical phase is the second one where the k-vertex disjoint paths toeach node in the vicinity are found according to the optimality criteria including the total costof the path, maximum edge cost in the path and number of hops. The authors use a function ofthese three parameters to select among the candidate disjoint paths which are found using theshortest path algorithm. However to determine the weight of these parameters for differenttopologies they have to carry out some experiments which decreases the practicality of thealgorithm. They use a greedy approach which selects the shortest path between two nodesin the vicinity and remove the nodes that are in this path and continue finding the next short-est path in the remaining set of nodes. This approach does not result the optimum solutionas expected. In the last stage of the algorithm, the transmission ranges of each node is ad-justed according to the topology constructed in the second phase. The difference between thiswork and ours is that they focus on the k-connectivity between any two nodes in the network

19

whereas we focus on the k-connectivity between sensor nodes and the set of supernodes in thenetwork. This difference dramatically changes the problem and the possible set of solutions.

Cardei et al [51] addresses fault-tolerant topology control in a heterogeneous wireless sen-sor network with two layer network architecture where the upper layer consists of severalresource-rich supernodes which are used for data relaying on top of a layer of large numberof energy constrained wireless sensor nodes. They also introduce the problem that we willalso focus in this work called the k-degree Anycast Topology Control (k-ATC) problem whichaims to adjust transmission ranges of the sensor nodes in order to achieve k-vertex supernodeconnectivity and minimize the maximum transmission power of the sensor nodes.

The main objective of the work is to maintain k vertex independent paths from the sensornodes to the set of supernodes with minimum transmission power. Authors propose a greedycentralized algorithm (GATC) which results the optimal solution and a distributed algorithm(DATC) that provides k-vertex supernode connectivity by incrementally adjusting the sensortransmission range. They perform simulations to show the performance of the GATC andDATC algorithms with various parameters. We will compare our solutions with the solutionspresented in this work. Now we will briefly discuss the algorithms the GATC and DATCintroduced in [51].

The algorithm GATC starts with a graph G which is already k-vertex supernode connectedwhich means there are at least k vertex disjoint paths from each sensor node to at least onesupernode. The GATC first makes some transformations on G to obtain a reduced graph Gr

where all supernodes are replaced with a single root node. In this reduced graph all edgesbetween sensor nodes are preserved but the edges between sensor nodes and supernodes areswitched to an edge between the sensor nodes and the root node. If a sensor node is connectedto more than one supernodes in G, only one edge is added in Gr which has the lowest cost.Another transformation is done to obtain the directed version of the reduced graph G−r . In thistransformation for all undirected edges between sensor nodes in Gr, two directed edges areadded in G−r . An edge between a sensor node and a supernode is changed with one directededge, from sensor node to supernode. After these transformations, authors show that anyheterogeneous WSN is k-vertex supernode connected if and only if corresponding reducedgraph is k-vertex supernode connected to the root.

After the transformations, the GATC sorts all the edges in G−r according to their costs whichare defined in terms of length of the edges. Edges are examined in decreasing order of costand an edge (u, v) is removed if node u remains k-vertex connected to the root. After exam-ining all the edges and removing the edges which do not affect the k-connectivity, the GATCadjusts transmission power of each node according to the new set of neighbors in the resultingtopology.

The GATC algorithm is mostly of theoretical importance since it is not practical to apply itfor large scale wireless sensor networks due to the requirement of global topology knowledge.However, it is a good point of reference for comparison with other algorithms since it gives theoptimal solution. We will be using the GATC algorithm for comparison with the algorithmswe propose.

Cardei et al [51] proposes another algorithm called DATC which is a distributed and hence amore practical solution for k-ATC problem. This algorithm requires only 1-hop neighborhoodtopology information which may also be extended to h-hop as well. In the DATC algorithm,each node i starts with a transmission power pmin

i , which is required to reach the first k neigh-

20

c

11111111a b

d

e f

g

Figure 3.1: Initially node a’s transmission range is set as to reach its k closest neighbors.

bors. If pmini is equal to pmax

i then no improvement can be done for node i, where pmaxi is

the maximum transmission power for node i. Otherwise, transmission power is incrementallyincreased for node i, to reach at least one neighbor from reachable neighborhood and it ischecked to see if all nodes in the reachable neighborhood are directly reachable from i ork-vertex connected to node i. If it is so, then the final transmission power is found for nodei, otherwise the iterative process is repeated until the transmission power is equal to pmax

i inthe worst case. In a 1-hop neighborhood, the chance of finding k-vertex disjoint paths be-tween a node and any of its neighbors is relatively low, especially for sparse networks. Thisis due to the limited number of alternative paths in such a small neighborhood. This situationcauses incrementing the transmission power to cover the nodes that are not reachable throughk-vertex disjoint paths in the 1-hop neighborhood. To obtain lower transmission power val-ues, an h-hop version of DATC is also proposed, but this causes the message complexity toincrease rapidly, resulting in significantly more energy consumption than 1-hop version.

The objective of the DATC algorithm is to make sure that any neighbor u, in the reachableneighborhood of any node v is either directly reachable from node v or there are k-vertexdisjoint paths from v to u. This condition ensures the k-vertex supernode connectivity of theresulting topology. This is proved by the authors in [51].

A sample run of the DATC algorithm for k = 2 using a 1-hop neighborhood local informationis shown in Figures 3.1 through 3.5. In Figure 3.1, node a and its 1-hop neighbors are shown.Circles centered at node a depict the distance of each neighbor to node a and thus the requiredtransmission range for reaching a neighbor on a circle. Initially node a adjusts its transmissionrange as to reach its k = 2 closest neighbors, namely, b and c. It is because for k-vertexsupernode connectivity each node in the network must have at least k neighbors. The circlethat represents the initial transmission range of node a is shown in red in Figure 3.1.

The next step in the DATC algorithm is to check whether the next closest neighbor, namely d,can be reached via two disjoint paths from node a using only the nodes that are in the currenttransmission range of node a which are the nodes b and c. As seen in Figure 3.2 node d can

21

11

d

111111a b

c

e f

g

Figure 3.2: Node a has two disjoint paths to node d, so its transmission range stays the same.

be reached via two disjoint paths a − c − d and a − b − d, so node a does not need to increaseits current transmission power because it does not have to directly reach node d. There nodea’s transmission range stays the same in this step.

The DATC algorithm proceeds by checking the remaining 1-hop neighbors that are reachablewith maximum transmission power. So the next neighbor is node e. With the current transmis-sion range, node e is not reachable directly. With the current local 1-hop topology of node a,there does not exist any paths to node e from node a. Therefore, the only option is to increasethe current transmission range of node a to reach node e directly. Figure 3.3 shows the trans-mission range of node a after this step. Note that, after changing the transmission range, nodea have to notify its neighbors by broadcasting a message that contains the new transmissionrange, because it affects the local neighborhoods of the neighboring nodes. Actually, everynode has to maintain transmission range and location of each neighbor that are reachable withmaximum transmission power. Otherwise, a node cannot compute the connectivity betweenany two 1-hop neighbors.

The next closest neighbor is node f which can be reached via two disjoint paths, namely,a−d− f and a−b− f as shown in Figure 3.4. So there is no need to increase the transmissionpower in this step.

The last node to consider is node g. Node a can compute at least two disjoint paths to nodeg using the local topology information as shown in Figure 3.5. Again in this step the trans-mission range of node a stays the same. This is the final transmission range for node a. Nowit is guaranteed that any 1-hop neighbor of node a can be reached directly or via at least 2disjoint paths from node a. This condition ensures the k-vertex supernode connectivity of theresulting topology as proved in [51].

The weak point of the DATC algorithm is that it requires testing for k-connectivity in eachpower increment step for each neighbor. This test requires complete topological view of 1-hop neighborhood which is not very expensive to obtain but it is a very small set of verticesto check k-connectivity. For 1-hop neighborhood most of the time, there will not be k-vertex

22

11

e

d

111111a b

c

f

g

Figure 3.3: Node a’s transmission range is increased to reach node e.

11

fe

11

d

1111a b

c

g

Figure 3.4: Node a has two disjoint paths to node f , so its transmission range stays the same.

23

11

g

e

11

d

1111a b

c

f

Figure 3.5: Node a has two disjoint paths to node g, so its transmission range stays the same.

disjoint paths between a node and its neighbor and the algorithm will result with pmaxi . In order

to obtain lower transmission power values, authors also propose an h-hop version of DATCbut in this case the message complexity of the algorithm will increase which will cause moreenergy consumption according to 1-hop version.

Our algorithm differs from DATC by the approach that we adopt for discovering vertex dis-joint paths. In DATC, each node starts with a minimal set of neighbors and minimal powerlevel. The power level is increased incrementally and only the paths from the neighborhoodthat are reachable with that power level can be discovered. The nodes outside of the reachableneighborhood are totally unknown to the node performing discovery and thus they are out ofthe search scope for discovering paths. This is an important limitation for DATC because ithas a low chance to find k-vertex disjoint paths for its neighbors in its reachable neighbor-hood, which typically has nodes that are in 1 or 2 hops distance from the node performing thediscovery. In contrary to DATC, in our algorithm, a sensor node can discover paths includingnodes outside of its reachable neighborhood. This is achieved by storing full path informationfrom supernodes to sensor nodes in local information tables. In this way, the DPV algorithmhas more chance to discover better k-disjoint paths than DATC. Another difference of ouralgorithm from DATC is that, we decrease the power level only after deciding the final topol-ogy. During path discovery in the DPV algorithm, nodes operate with maximum power, thus,increasing the likelihood of discovering more paths than DATC. Our simulation results are inconformity with this discussion.

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CHAPTER 4

PROPOSED WORK: DISJOINT PATH VECTOR ALGORITHM

4.1 Overview

In this thesis, we propose an algorithm for fault tolerant topology control in two tiered hetero-geneous wireless sensor networks consisting of resource rich supernodes and simple sensornodes which have batteries with limited capacity. In order to obtain fault tolerant topologieswe will focus on k-vertex supernode connectivity which is defined in by Cardei et al in [51].In a k-vertex supernode connected topology, each sensor is connected at least one supernodeby k vertex disjoint paths. Such topologies are tolerant to k-1 node failures at worst case. Inother words, sensor nodes remain connected to supernodes when up to k-1 sensor nodes areremoved from the network.

We propose an algorithm named Disjoint Path Vector (DPV) algorithm which is based onthe observation that we can remove the edges with the neighbors which are not on one ofthe k-vertex disjoint paths to supernodes. In order to achieve this, we need to determinewhich neighbors are on one of such paths and which are not. We will show how the DPValgorithm enables us to find a superset of the required vertices in order to guarantee the k-vertex supernode connectivity.

The objective of DPV is to minimize the total transmission power of the nodes in the network.The DPV algorithm is run by each sensor in a distributed manner with locally collected data.Using this data each node computes the set of required neighbors that guarantees k-vertexsupernode connectivity. The changes in the neighbor lists are exchanged in an efficient wayto keep the message overhead small. Having found the required neighbors, each node removesits edges which are not connected to a required node in coordination with its neighbors. Thento save energy, we use power adjustment technique to decrease the transmission range of thesensor nodes so as to reach to the furthest node in the new set of neighbors.

The DPV is a distributed algorithm executed by each sensor node in the network. Each nodemakes use of the topology information in the local 1-hop neighborhood. The paths to thesupernodes are explored by using messages initiated by the supernodes that carry the traversedpath information from a supernode to a sensor node. Global network topology information isnot required by the DPV algorithm.

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4.2 Sample Scenario

Consider a weapon system composed of artillery units installed on the country border forhomeland security. This weapon system is integrated with a 2-tiered heterogeneous wire-less sensor network where supernodes are located on the artillery units. Artillery units aresteerable so they can head toward the targets whose locations are known. The data gatheredby sensor nodes are forwarded to supernodes where this data is evaluated and a decision onwhether to open fire or not is taken. The sensor nodes are deployed in the area to detect po-tential intrusion activities. When an activity is detected by a sensor node, it forwards this datato supernodes for evaluation and execution of proper action. In this scenario, supernodes havemore power capacity and more sophisticated technical facilities (e.g. camera, IR sensors)which enables accurate target classification compared to ordinary sensor nodes. So they aremore expensive than ordinary sensor nodes and number of supernodes is much lower than theordinary ones.

In this scenario, it is very critical to deliver the data sensed by the sensors to supernodes. Itis also common to lose some sensor nodes because of energy depletion, harsh environmentalconditions, hostile activities of intruders or artillery strikes. Therefore a network topologywhich is tolerant to a certain number of node failures is required. So it is desired that a sensornode should have more than a certain number of independent paths to supernodes. It is alsopossible to loose supernodes due to intruder attacks. It would be better to have connectionswith more than one supernodes in order to remain connected to at least one super node in caseof a supernode loss or failure. Since the sensor nodes are energy constrained, it is essentialto have an energy efficient topology control mechanism in order to obtain a longer networklifetime.

Our work targets the topology control problem designated by the above sample scenario. Weare looking for a distributed, fault tolerant and an energy efficient topology control algorithmfor 2-tiered heterogeneous wireless sensor networks.

4.3 Network Model

We consider a heterogeneous WSN consisting of M supernodes and N sensor nodes, withM << N. N sensor nodes are randomly distributed in the 2D plane. M supernodes are de-ployed at known locations manually. We are interested in sensor-sensor and sensor-supernodecommunications only. We do not model the supernode-to-supernode communications. We as-sume that supernodes are not energy constrained so they can directly communicate with a basestation or they can send the data collected from sensors to other supernodes if necessary. Wealso assume that all supernodes are identical which means delivering a message to any of thesupernodes is sufficient and considered as a successful delivery. In the initial network topol-ogy each energy constrained sensor node has the transmission range Rmax. We assume thatsupernodes have transmission ranges long enough to communicate with the base station andany other supernode in the network.

We represent the initial network topology with an undirected weighted graph G = (V, E)where V = {v1, v2, ..., vN , vN+1, ..., vN+M} is the set of nodes and E = {vi, v j | dist(vi, v j) < Rmax}

is the set of edges where dist(vi, v j) depicts the distance between nodes vi and v j. The first Nnodes in V are the energy constrained sensor nodes and the last M nodes are the resource rich

26

Figure 4.1: A Sample 2-Tiered WSN.

supernodes.

An example network topology is given in Figure 4.1 with 4 supernodes and 20 sensor nodesdeployed in a 300 x 300 unit square area where Rmax is set to 110 units.

4.4 Problem Definition

We aim to construct and maintain a k-vertex supernode connected network topology in orderto route the data sensed by the sensor nodes to the supernodes for two tiered wireless sensornetworks with network model given in section 4.3. We model topology control as a trans-mission range assignment problem for each sensor node in the network. The objective is tominimize the assigned transmission power for all sensors while maintaining k-vertex disjointpaths from each sensor to the set of supernodes. In this topology, each node should only keepnecessary set of neighbors which satisfy k-vertex supernode connectivity. Each sensor nodein the network must be connected to at least one supernode with k vertex disjoint paths.

Before formulating the problem we give some necessary definitions:

Definition 1 (Vertex disjoint paths): Set of paths with common end points that have no othervertices in common. In this work all disjoint paths are vertex disjoint paths unless otherwisestated.

Definition 2 (k-vertex supernode connectivity):A WSN is k-vertex supernode connected if,for any sensor node n ∈ V , there are k pairwise vertex disjoint paths from n to one or moresupernodes. In other words, a WSN is k-vertex supernode connected if the removal of any k- 1 sensor nodes does not partition the network [51].

We can now define the problem as follows:

27

Given a k-vertex supernode connected WSN with M supernodes and N energy-constrainedsensor nodes that can adjust their transmission range up to a predefined constant Rmax, de-termine the transmission range of each sensor such that the total transmission power is min-imized and the resulting topology is still k-vertex supernode connected. Next, we state theproblem definition more formally.

Definition 3(Problem definition): Given an undirected graph G = (V, E) where V is the setof all vertices and E is the set of all edges and given two disjoint subsets of vertices namelyM ⊂ V , N ⊂ V and M ∩ N = ∅, where there exists at least k-vertex disjoint paths from eachvertex v ∈ N to the set of vertices M, find set of edges F such that G(V, E − F) satisfies thefollowing:

1. There exist at least k-vertex disjoint paths from each vertex v ∈ N to the set of verticesM.

2.∑N

i=1 pi is minimized, where pi is the weight of the maximum weighted edge ∈ (E − F)of vi ∈ N.

4.5 Disjoint Path Vector Algorithm for k-vertex Supernode Connectivity

Our algorithm named Disjoint Path Vector algorithm (DPV) efficiently assigns transmissionpower levels for sensor nodes while preserving the k-vertex supernode connectivity of thenetwork in a distributed and localized manner. It consists of five main stages as shown in4.5.1. The first stage is path information collection, initiated by the supernodes through INITmessages. An INIT message contains the ID of the supernode that created the message andcan only be transmitted by a supernode. These messages are received by the sensor nodes inthe network and each receiver node updates its local path information according to that data.Sensor nodes transmit PathIn f o messages when an update occurs in their local disjoint pathlists. Upon receiving a PathIn f o message, each sensor node extracts the disjoint paths tothe supernodes by using its local data and the path information received from the PathIn f omessage. If the incoming PathIn f o message improves the cost of the disjoint paths, themessage is forwarded by adding the updated path information. The cost of a set of disjointpaths is defined as the maximum of the costs of the paths in the set. When improvement is notpossible, the first stage of the algorithm ends and the second stage starts in which each nodecalculates its required neighbors using the locally found set of disjoint paths as the input.

In the third stage, for each disjoint path a NOT IFY message is initiated by each sensor nodeand forwarded along the nodes in the path. Neighbor nodes in a disjoint path mark each otheras a required neighbor. In the fourth stage, neighbors that are not selected as required areremoved from the neighbor list. In the final stage, each node adjusts its transmission powerlevel to reach its farthest required neighbor according to the new topology that resulted fromthe removal of the non-required nodes. We now give a detailed explanation for each stage ofthe DPV algorithm.

After deployment of sensor nodes and supernodes, the first stage of the algorithm is initiatedby INIT messages which are broadcasted by super nodes through the network. An INITmessage contains the ID of the supernode which created the message. INIT messages can onlybe transmitted by supernodes. Any sensor node which receives an INIT message, updates its

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Algorithm 4.5.1 Five Main Stages of DPVInput: Set of all neighborsOutput: Superset of required neighbors

1: Collect path information and calculate disjoint paths (Procedures 4.5.2 and 4.5.3)2: Calculate the set of required neighbors (Procedure 4.5.4)3: Notify the nodes in the disjoint paths and update the required neighbors (Procedure 4.5.5)4: Remove the neighbors that are not marked as required in coordination with 1-hop neigh-

bors5: Reduce power level such that it is sufficient to reach the farthest neighbor

Table4.1: Path Information Table at node y. Node y holds 3 paths to supernodes.

Supernode Path Path Cost

B y-B 230A y-z-x-A 250C y-z-C 300

local path information table by adding an entry for the path to super node which sent the INITmessage. In this special case such an entry will only include the ID of the supernode and thecost of the link between the receiver node and supernode. The cost will be the length of thelink. In general, an entry in the local path information table in a sensor node will include apath to a supernode and the cost of that path which is selected to be as the length of the longestlink of the path. Paths are sorted according to the cost in ascending order in the local pathinformation table. An example of the path information table is given in Table 4.1.

Details of the distributed algorithm run by each sensor node in the information collectionstage is given in Algorithm 4.5.2. The DPV algorithm notations are introduced in 4.2.

Procedure 4.5.2 Path Information Collection in DPVInput: I, L, kOutput: D1: T ← ∅;2: for all received PathInfo message I do3: if I.Sender is a supernode then4: r ← new Path(I.Sender);5: if r < T then6: T ← T ∪ r ;7: Transmit PathInfo(T );8: end if9: else10: D←MIN_DIS_SET(T ); (Procedure 4.5.3)11: c← Cost(D);12: U ← I.T ∪ T ;13: Sort(U);14: T ′ ← {pi ∈ U | i <= L} ;15: D′ ←MIN_DIS_SET(T ′); (Procedure 4.5.3)16: c′ ← Cost(D′);17: if c′ < c then18: T ← T ′;19: Transmit PathInfo(T );20: end if21: end if22: end for

Having updated the local path information table, a sensor node creates and transmits a PathIn f omessage, which contains its ID and path information table. A PathIn f o message can only be

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Table4.2: DPV Notations.

T and T ′ Set of local pathsD and D′ Set of disjoint paths with the minimum costU Union of two sets of pathsI Received PathInfo messageL Maximum number of paths to be storedc and c′ Cost of disjoint pathsr, t, p and pi Variables referencing pathsk Degree of disjoint connectivityR Set of required neighborsS Set of first k disjoint pathsB Set of neighbors of a nodeΦ Incoming Notify messagen Variable referencing a nodeQ Set of all subsets of T of size kq A subset of T of size kqmin Minimum cost subset of T of size kd A temporary boolean variable

sent by sensor nodes where an INIT message can only be sent by super nodes. INIT mes-sages contain only ID of the sending supernode where a PathIn f o message includes pathsto supernodes and their costs. Sensor nodes transmit PathIn f o messages to their reachableneighborhood using maximum power. Any sensor node that receives a PathIn f o messagecalculates the union of the existing and the received paths via PathIn f o message. Then, theset of disjoint paths with the minimum cost is calculated for the existing paths and for thenewly calculated union. Notice that the size of calculated disjoint sets is at most k, becausewe need only k disjoint paths. If the new cost is lower than the current cost, the local pathinformation table is updated. The algorithm for finding disjoint paths run by each sensor nodeis given in Procedure 4.5.3. The resulting list of disjoint paths is stored for use in the nextstages of the DPV algorithm.

Any sensor node that updates its local path information table transmits a PathIn f o messagethat contains the updated path information table. Note that if a PathIn f o message does notcause an update in the receiver node’s disjoint paths list, then no PathIn f o message is sent.This condition ensures the termination of the path information collection stage. If furtherimprovement on the path costs is not possible, transmission of PathIn f o messages stops. TheDPV algorithm is guaranteed to converge because there is an upper bound on the number ofPathIn f o messages that any sensor can send during the path information collection stage. APathIn f o message is only transmitted if an update occurs in the local set of disjoint paths.An update can only occur if a lower-cost disjoint path is discovered via a received PathIn f omessage. At the worst case, there can be |E| different-cost disjoint paths from a sensor nodeto the set of supernodes where |E| is the number of edges in the network given that cost ofa path is defined as the cost of the longest edge in that path. In the worst scenario, these |E|different-cost disjoint paths can be discovered in the decreasing order of path cost. Suppose

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Procedure 4.5.3 Finding Disjoint Paths to Supernodes (MIN_DIS_SET)Input: T and kOutput: D1: D← ∅;2: if |T | > k then3: Q← { q ⊂ T | |q| = k };4: c← ∞;5: qmin ← ∅;6: for all q ∈ Q do7: if q consists of disjoint paths then8: if Cost(q) < c then9: c← Cost(q);10: qmin ← q;11: end if12: end if13: end for14: D← qmin;15: else16: for all t ∈ T do17: d ← true;18: for all q ∈ D do19: if t ∩ q , ∅ then20: d ← f alse;21: break;22: end if23: end for24: if d = true then25: D← D ∪ t;26: end if27: end for28: end if

that each discovery results an update, then the node will at most send |E| PathIn f o messages.Since a graph can have at most O(N2) edges, where N is the number of nodes, we concludethat any sensor node can transmit at most O(N2) PathIn f o messages.

We set an upper limit on the number of hops a PathIn f o message can traverse during the pathinformation collection stage. This is the PathIn f o message’s time-to-live (TTL) value, and itdirectly affects the number of hops in the resulting paths. This value is set at the supernode thatsends the INIT message and it is included in every PathIn f o message. When a sensor nodereceives a PathIn f o message that has reached the TTL value, no further PathIn f o messageis created even if an update occurred as a result of this PathIn f o message. This approachensures that paths with a length above a certain limit are not considered in the disjoint pathcalculation; it can be considered as a prepruning that occurs before determining the set ofdisjoint paths with minimum cost.

Figures 4.2 through 4.11 show a sample run of the path information collection stage of theDPV algorithm on a sample network topology with local path information tables and disjointpaths for each sensor node.

As in Figure 4.2, path information collection is initiated by the INIT message sent by supern-ode A. Because supernode A has only one neighbor x, this message is only received by sensornode x. Upon receiving the message, node x calculates the path x − A and its cost (90) andstores it in its local path information table. In this case there is only one path in node x’s tableand thus this path is the only possible disjoint path for node x. As the disjoint paths of nodex are updated, the node will create a PathIn f o message containing its path information tableand send it to its 1-hop neighbors. Node x has only one neighboring sensor node, namely z,hence node x’s PathIn f o message will only be received by node z.

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A x-A 90

z

C

y

x A

B

Supernode

Sensor node90

19070

230

210

250

280

200

Path information tables maintained by sensor nodes

x-A 90

Max Cost 90

x

Disjoint Paths Disjoint Paths Disjoint Paths

y z

Figure 4.2: Path information tables after supernode A transmits an INIT message.

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Figure 4.3 shows the transmission of node x to node z. The path information tables and dis-joint paths present the updated and final situation after node z receives the PathIn f o messagesent by node x and corresponding path calculations. Because there was only one path (x − A)in node x’s path information table, the PathIn f o sent by node x contains only this path andits cost. After receiving this information, node z calculates the path from itself to supernodeA and its cost. The resulting path and its cost are stored in node z’s path information table.The only path in this table is also the only disjoint path that node z currently has. Since anupdate occurred in its disjoint paths, node z will transmit a PathIn f o message to its 1-hopneighbors to notify them of this update. Node z has two neighbors, namely x and y, but node zwill transmit its PathIn f o message only to node y, because the previous message that causedthe update was sent by node x, so there is no need to send this message to node x. In general,a sensor node does not send a PathIn f o message to the neighbor from which it had receivedthe last PathIn f o message.

A x-A 90

A

z

C

y B

Supernode

Sensor node90

19070

230

210

250

280

200

x


x-A 90

Max Cost 90

x


y z

A z-x-A 250

z-x-A 250

Max Cost 250

Figure 4.3: Path information tables after node x transmits a PathIn f o message to node z.

Figure 4.4 shows the transmission of the PathIn f o message from node z to node y. Thismessage contains path z− x−A and its cost 250. Before this message was received, there wasno path in node y’s path information table, therefore node y updates its table by calculating thepath for itself. Note that path costs are determined by the most costly link in the path. Here,the most costly link in path y − z − x − A is z − x, with a cost of 250, and thus the path costis also 250. This is again the only disjoint path for node y. Although node y has an updated

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disjoint path list now, it does not transmit a PathIn f o message because it was node y’s onlyneighbor (node z) that caused this update. Therefore, node y does not make any transmissionin this case.

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Max Cost 250

Figure 4.4: Path information tables after node z transmits a PathIn f o message to node y.

Transmission of INIT message from supernode B is shown in Figure 4.5. Supernode B has 3neighbors (x, y, z) and all of them receive this INIT message and update their path informationtables accordingly. All updated paths and disjoint paths are shown in red after the update. All3 sensor nodes, insert a new path into their path information tables which includes a direct linkto supernode B. Calculation of disjoint paths results 2 disjoint paths for each node as shownin Figure 4.5. Since all 3 nodes update their list of disjoint paths, all of them need to transmitPathInfo messages to their one hop neighbors. In this sample run, we neglect the order of thePathInfo messages sent, we simply follow the alphabetical order of the node names. Note thatthe intermediate steps of the path information collection stage are dependent on the order ofthe messages transmitted. We will continue with the node z’s transmission in the next step.

In Figure 4.6 we see the results of PathInfo transmission of node x to node z. This transmissionbrings a new path for node z that is z − x − B. However this path is has the same cost withan already existing path and thus it does not make an improvement on the cost of the disjointpaths. Therefore node z does not need to make a PathInfo message transmission for thisreception. However node z had already updated its disjoint paths after the supernode B’s

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A x-A 90

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Max Cost 250

z-B 70

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Max Cost 250

Figure 4.5: Path information tables after supernode B transmits an INIT message.

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transmission in the previous step (Figure 4.5). So the next step continues with the transmissionof node z.

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A z-x-A 250

B z-x-B 250

y-B 230

y-z-x-A 250

Max Cost 250

z-B 70

z-x-A 250

Max Cost 250

Figure 4.6: Path information tables after node x transmits a PathIn f o message to node z.

Node z transmits its PathInfo message containing its path information table to its neighborsx and y. Node x inserts a new path namely x − z − B to its path information table and nodey adds 2 new paths y − z − B and y − z − x − B. The update that occurred in node x’s pathinformation table does not cause an update in the disjoint path list because node x has already2 disjoint paths both of which are cheaper than the last added path. Note that in this samplerun, k value is 2 so we only keep 2 disjoint paths where the total cost is minimum. Howeverwe see a different picture for node y. The path y− z− B has the cost 210 and it is the cheapestpath among all paths in the path information table of node y. Therefore it causes an update inthe disjoint paths of node y. The path y− z− x−A with cost 250 is removed from disjoint pathlist and y − z − B with cost 210 is added instead. Node y does not need to make a PathInfotransmission to node z regarding to this update because it is already caused by node z but stillit has to transmit a PathInfo message associated with the update caused by the supernode B’stransmission depicted in Figure 4.5.

Figure 4.8 illustrates the case where node y makes a PathInfo transmission after the updatecaused by the supernode B’s INIT message transmission. As a result of this PathInfo messagenode z finds out the path z − y − B with cost 230 and it updates its path information table and

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Max Cost 230

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Max Cost 250

Figure 4.7: Path information tables after node z transmits PathIn f o message to nodes x andy.

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disjoint paths. The more costly path z − x − A is replaced with the cheaper path z − y − B asseen in Figure 4.8. Since node z’s disjoint paths have been updated, now node z will transmita PathInfo message to node x. Again, PathInfo message will not be sent to node y because itwas the node that sent the last PathInfo message which caused this update.

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A z-x-A 250

B z-x-B 250

y-z-B 210

y-B 230

Max Cost 230

z-B 70

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Max Cost 230

Figure 4.8: Path information tables after node y transmits a PathIn f o message to node z.

As shown in Figure 4.9 node z’s transmission to node x causes an update in the path infor-mation table but this change does not affect the list of disjoint paths, because the new pathx−y− z−B is more costly than the existing disjoint paths. Therefore node x does not transmita PathInfo message in this case.

The path information collection stage of the sample run of the DPV algorithm continues withthe INIT message transmitted by the supernode C in Figure 4.10. Supernode C has twoneighbors namely x and z. The INIT message received by node x does not make a change onthe list of disjoint paths as the link x − C has a high cost (280). On the other hand, the INITmessage received by the node z does make a difference. The new path z −C has a cost of 200which is the second cheap path in the path information table of node z. Calculation of disjointpaths for node z results the paths z− B and z−C. As a consequence of this update node z willagain need to transmit a PathInfo message.

In Figure 4.11 we see the final PathInfo transmission made by node z. As seen from the pathinformation tables there is one new path for node x and one for node y. However none of

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Max Cost 230

z-B 70

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Max Cost 230

Figure 4.9: Path information tables after node z transmits a PathIn f o message to node x.

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xDisjoint Paths Disjoint Paths Disjoint Paths

y z

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Figure 4.10: Path information tables after supernode C transmits an INIT message.

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these paths makes a difference on the list of disjoint paths as demonstrated in Figure 4.11.So there will not be any PathInfo transmissions regarding to this step. Since all 3 supernodeshave transmitted their INIT messages and all corresponding PathInfo transmission are over,the path information collection stage of the DPV algorithm ends. The disjoint paths shown inFigure 4.11 are the final disjoint paths for the nodes x, y and z.

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xDisjoint Paths Disjoint Paths Disjoint Paths

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Figure 4.11: Path information tables after node z transmits PathIn f o message to nodes x andy.

Having found the disjoint paths, each sensor node now creates its required neighbor list.These are the neighbors where a disjoint path starts from. A node v holds path information toa supernode A, as a sequence of node ID’s that constitute the path as seen in Disjoint Pathstables in Figure 4.12. So the first ID in the sequence represents the current node and the nextID represents the first node u of the path to the supernode A. In other words, when node vwants to send a message to the supernode A, the message will be forwarded through the nodeu. If such a path is one of k best disjoint paths of node v, then node u is labeled as a requiredneighbor of node v. Since we aim to come up with a bidirectional network, node v is alsolabeled as required neighbor for node u as well. For instance, node y has two disjoint pathsnamely y − z − B and y − B. For the disjoint path y − z − B node z is the starting point of thepath because it is the next node after y. Therefore node z is a required neighbor for node y.In the same manner, supernode B is also a required neighbor for node y. Required neighborsfor all sensor nodes are shown in in Figure 4.12. A link with a required neighbor is shown

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in red. Procedure for finding the required nodes which is run by each sensor node is given inAlgorithm 4.5.4.

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Required Neighbors Required Neighbors Required Neighbors

{A,B} {z,B} {B,C}

Figure 4.12: Disjoint paths and required neighbors for all sensor nodes after the path infor-mation collection stage.

To guarantee that all nodes in a selected disjoint path are labeled as required neighbors, weneed to notify all the nodes on that path. To achieve this, each node sends a NOT IFY messagefor each of its selected disjoint paths. A NOT IFY message is forwarded along the disjointpath for which it was created. Each neighboring node in the disjoint path marks each otheras required neighbors. This stage ensures that any node on a selected disjoint path will bemarked as a required neighbor of its neighbors that are also on the same disjoint path. Ifany two neighbor nodes do not mark each other as required neighbors, it means that the linkbetween these two nodes is not necessary and can be removed. Procedure 4.5.5 shows thesteps taken by each sensor node upon receiving a NOT IFY message.

For a node which do not have the path information of at least k vertex disjoint paths to su-pernodes, all neighbors are defined to be required because in that case it is not known whichneighbors can be given away. Such a node cannot decide which neighbors are required andwhich are not because it has not enough information locally. In that case all neighbors are keptbecause all of them can potentially be part of a disjoint path connecting some sensor nodesto supernodes. This approach ensures the k-vertex supernode connectivity of the resultingnetwork topology in case of insufficient amount of local information.

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Procedure 4.5.4 Finding Required NeighborsInput: D and kOutput: R1: R← ∅;2: S ← ∅;3: if |D| >= k then4: Sort(D);5: S ← {pi ∈ D | i <= k};6: for all p ∈ S do7: R← R ∪ p.First;8: end for9: end if10: for all p ∈ S do11: Transmit Notify(p);12: end for

Procedure 4.5.5 Updating Required Neighbors By Noti f y MessagesInput: R, B and Φ: Incoming Notify messageOutput: R: Updated set of required neighbors1: for all received Notify message Φ do2: for all Node n ∈ Φ.Path do3: if n ∈ B then4: R← R ∪ n;5: end if6: end for7: end for

Having determined the final set of neighbors, each node adjusts its transmission power as toreach its furthest neighbor according to the new topology which came out after the removalof neighbors that are not required. This is the last stage of the DPV algorithm.

The resulting topology generated by applying the last stage of the DPV algorithm to thesample network topology is shown in Figure 4.13. The link between nodes z and x is removed.Also the link between the supernode C and node x is removed. All the sensor nodes in thenetwork are connected to at least one supernode with 2-vertex disjoint paths.

Theorem 1 (Correctness): If G is k-vertex supernode connected then the final topologygenerated by the DPV algorithm is a k-vertex supernode connected topology.

Proof: Let us assume that the current graph is k-vertex supernode connected and that an edge(u, v) is removed. Consider any sensor node n. It is k-vertex supernode connected before theremoval of edge (u, v), which can only happen in the DPV algorithm when neither u nor vmark each other as required. Note that both u and v have k-vertex disjoint paths to at leastone supernode that does not contain node v and u, respectively. After the removal of (u, v) itis thus guaranteed that both u and v will remain k-vertex connected to at least one supernode;otherwise the DPV algorithm would not remove the edge (u, v). If removal of an edge (u, v)does not break the k-vertex supernode connectivity of node u and v, it is guaranteed that theresulting topology will be k-vertex supernode connected as proved in [51]. Therefore, weconclude that the DPV algorithm results in a topology where all sensor nodes are k-vertexsupernode connected.

Theorem 2 (Bidirectionality): If the links in the initial network topology is bidirectionalthen the final topology generated by the DPV algorithm is also bidirectional.

Proof: In the initial network topology, all the links are bidirectional. The algorithm DPVremoves a link between a pair of nodes only when both nodes agree that they are redundantneighbors to each other. So before removing an edge (u, v) the DPV algorithm makes sure

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z

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Nodes x, y and z have at least 2 node-disjoint paths

to the set of supernodes

Figure 4.13: The final topology resulted after the application of the DPV algorithm.

that u is in the redundant list of v and v is in the redundant neighbor list of u. This meansan edge can only be removed in agreement of both nodes. If this condition is not met noneof the nodes remove its neighbor. So it is not possible to have any unidirectional links in thetopology generated by the DPV algorithm. Therefore we conclude that the DPV algorithmalways generates bidirectional topologies.

4.6 Time Complexity Analysis of the DPV Algorithm

The execution of the DPV algorithm is initiated by the INIT messages transmitted by supern-odes. INIT messages can only be transmitted by supernodes and they contain the ID of thetransmitting supernode. Any sensor node that receives an INIT message simply calculatesthe path cost between the transmitting supernode and the sensor node itself and adds this pathinto its local path information table. Since an update occurred in the local path informationtable of the receiving sensor node, this node now creates an updated PathIn f o message andtransmits it to its 1-hop neighbors. These steps takes constant time (1).

Sensor nodes receiving a PathIn f o message calculate the union of the local path informationand the received paths in the incoming message. The running time complexity of this stepdepends on the number of paths in the local path information table of the receiving node andin the incoming PathIn f o message. In the DPV the maximum number of paths that can be

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stored in a sensor node’s path information table is set to a constant value (p) because sensornodes have limited memory and limited processing power. Calculating the union of the twopath information tables takes O(p) time. Paths in the union are sorted in ascending order; thefirst p of the paths are kept and the others eliminated. Sorting takes O(plogp) time and gettingthe first p paths takes O(p) time (2).

Having formed the union of the path information tables, we now find the set of disjoint pathsof size k with the minimum cost. We achieve this by enumerating all subsets of paths of sizek and find the set with the minimum cost. Enumerating all these subsets takes O(pk) time and(pk) subsets are formed. For each subset we perform a disjointness test and find the disjointset with the minimum cost. This step takes O(kλpk) time, where λ is the maximum lengthfor a path in terms of number of hops. This parameter is also set to be a constant in the DPVand is a result of setting a TTL value for a PathIn f o message forwarded in the network. Inour experiments we set λ to 7 but it can be thought as a small constant compared to numberof sensor nodes in the network. Therefore, we conclude that upon receiving a PathIn f omessage a sensor node requires O(kλpk) time, where k, λ and p are constants (3). The stepby step running time analysis of the procedure for finding set of disjoint paths of size k withminimum total cost is given in Figure 4.14.

Upon receving a PathInfo message:

if The PathInfo message received directly from a super node

check the current PathInfoTable and {O(p)}

add this path if does not already exist {O(1)}

else

Calculate total cost of current disjoint paths {O(kλpk)}

Calculate union of current paths and received paths {O(p)}

Sort the paths in ascending order {O(plogp)}

Get first p paths in order {O(p)}

Calculate total cost of resulting disjoint paths {O(kλpk)}

if resulting cost is less than the current cost

change the receiver’s disjoint paths with the new set {O(p)}

endif

end if

if Any update is made on the receiver’s PathInfoTable

transmit a new PathInfo message {O(1)}

O(p)

O(kλpk)

O(1)

p : Maximum number of paths that can be stored by a node

k : Desired number of disjoint paths to super nodes per node

λ : Maximum number of hops for a path

Figure 4.14: Time Complexity Analysis of Finding Disjoint Paths.

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The calculated cost for the union is compared with the original disjoint path cost. If thenew cost is less than the previous cost, the node updates its local path information table andtransmits a new PathIn f o message that contains the updated path information. Calculatingthe cost for the original path information table is not necessary because it was calculated inthe last update. If a better set of disjoint paths is found then the path information table wouldneed to be updated. This step involves clearing the table and inserting the new paths into it,which takes O(p) time (4). The step by step running time analysis of the path informationcollection stage of the DPV algorithm is given in Figure 4.15.

Create an empty list DisjointPaths to hold disjoint paths {O(1)}

if Number of paths in PathInfoTable is greater than k

Find all subsets of size k for PathInfoTable {O(pk)}

Find the disjoint subset with minimum total cost {O(kλpk)}

Fill the DisjointPaths with the paths in min. cost subset {O(k)}

else

for each PathInfoRow in PathInfoTable do { max. k times}

IsDisjoint = TRUE

for each Path in DisjointPaths do { max. k-1 times}

if DP contains any node in PathInfoRow.Path {O(λ)}

IsDisjoint = FALSE

Break the loop

end if

end for

if IsDisjoint == TRUE

Add path PathInfoRow.Path to DisjointPaths {O(1)}

end if

end for

end if

O(kλpk)

O(k2λ)

p : Maximum number of paths that can be stored by a node

k : Desired number of disjoint paths to super nodes per node

λ : Maximum number of hops for a path

Figure 4.15: Time Complexity Analysis of Path Information Collection Stage.

After the path information collection stage, required neighbors are found. In this step eachsensor node traverses its disjoint path set and marks the first nodes of each path as required.In addition, it sends a notification message along each disjoint path to notify the nodes thatare on that path. Since there can be at most k such paths, this step takes O(k) time (5).

Having found the required neighbors, each sensor adjusts its transmission range accordingly.This step can be completed in O(k) time (6).

Above, we analyzed the running time complexity of the main steps of the DPV algorithm.The dominating step is (3), which finds the minimum-cost disjoint paths. Because this step

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takes O(kλpk) time, we conclude that any sensor that receives a PathIn f o message requiresO(kλpk) processing time at the worst case.

To determine the total running time for the algorithm to reach the final topology, we mustdetermine the maximum number of PathIn f o messages that a sensor node can receive duringthe execution of the DPV algorithm. As explained in Section 4.5, the upper bound on thenumber of PathIn f o messages that a node can transmit is O(n∆), where n is the numberof nodes in the network and ∆ is the maximum degree of a sensor node. Thus, a node canreceive at most O(n∆2) PathIn f o messages. Hence, total asymptotic running time of theDPV algorithm is O(n∆2kλpk) per node. Since the parameters k, λ and p are constant, DPV’srunning time complexity is O(n∆2).

In [51], the time complexity of the DATC algorithm is given as O(∆5). So, in dense graphswhere ∆ is high compared to n, DATC will experience much higher computation overheadthan the DPV algorithm. In the worst case, where there is an edge between every node,complexity of DATC will be O(n5) whereas our algorithm will be O(n3).

4.7 Message Complexity Analysis of the DPV Algorithm

During the execution of the DPV algorithm, messages are transmitted in four situations. Thefirst one occurs in the initiation phase, where supernodes send INIT messages. Each supern-ode sends one INIT message, therefore m messages are transmitted in this phase, where m isthe number of supernodes. However, we do not consider these messages because they are sentby supernodes, which have no power restrictions in our scenario. In addition, since m << n,where n is the number of sensor nodes, the asymptotic message complexity is not affected, aswe show below.

Table4.3: Time and message complexities of DPV and DATC per node.

Algorithm Time Complexity Message Complexity

DPV O(n∆2) O(n∆)DATC O(∆5) O(∆h)

The second case occurs when a path information update is made to the local path informationtable maintained by each sensor node. As discussed in Section 4.5, the upper bound on thenumber of PathIn f o messages that a node can transmit is O(n∆), where n is the number ofnodes in the network and ∆ is the maximum degree of a sensor node. Then, considering that anode has at most ∆ neighbors to receive from, the number of PathIn f o messages that a sensornode can receive is bounded by O(n∆2).

The third situation is node notification, which occurs on a selected disjoint path. A Noti f ymessage is transmitted for each selected disjoint path, and because a node can select at most kpaths, a sensor node initiates k Noti f y messages at most. Each Noti f y message causes λ − 1message transmissions, where λ is the length of a disjoint path in terms of number of hops.Therefore, at most a sensor node transmits k(λ − 1) Noti f y messages during this step.

From these calculations, we have O(n∆) messages and k(λ−1) Noti f y messages per node andthe total number of messages that a sensor node transmits in the worst case is thus O(n∆) +

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k(λ − 1). Eliminating low-order terms, we conclude that the asymptotic message complexityof the DPV algorithm is O(n∆).

The message complexity of DATC is reported as O(∆) per node in [51]. However this is validfor 1-hop neighborhood only. For h-hop neighborhood the complexity will be O(∆h), becauseeach sensor needs to forward the messages that it receives from its h-hop neighborhood. Onthe other hand, one can note that the worst case for the DPV algorithm, where paths arediscovered in the order of decreasing cost, is unlikely, since it is more probable to receivemessages first from shorter paths than the longer ones. Therefore, we expect a lower messagecomplexity in the average case. Our simulation results are in conformity with this analysis.Time and message complexity of the algorithms are summarized in Table 4.3.

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CHAPTER 5

EVALUATION

In this chapter we report the results of the experiments performed to evaluate our proposedalgorithm. We evaluate our algorithm by comparing it with GATC and DATC. algorithms. Inorder to achieve this, we implemented DPV, GATC and DATC algorithms by using a customevaluation framework which provides generating random network topologies, executing thealgorithms on the generated topologies, calculating the desired metrics and visualizing theoutputs of the experiments.

5.1 Evaluation Approach

The general approach that we follow for evaluating our algorithm is summarized in Fig-ure 5.1.1.

Algorithm 5.1.1 Evaluation Approach.1: for all Evaluation Scenarios S do2: for seed = 1 to n do3: Generate random network topology T using seed4: for all Topology control algorithms A do5: Run experiment with A for S on T6: Store the output in a table7: end for8: Calculate the average values of the stored result9: Write the average values into the output file

10: end for11: end for

This approach ensures that each algorithm is run on the same random topologies, so it preventsany biased results that may occur due to the specific topology of the network generated.

As summarized in Figure 5.1.1, for each scenario we run DPV, GATC and DATC algorithmswith different seeds, and for each experiment we output the results, namely total transmissionpower and total number of links in the resulting topologies generated by each algorithm, alsothe number of total transmissions and receptions required for execution of the algorithms.

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Table5.1: Simulation Parameters.

Deployment Area 600m × 600mPath Loss Exponent: α 2Initial Transmission Range of Nodes: Rmax 100mNumber of Sensors: N [100...500]Number of Supernodes: M 5% and 10% of NDegree of Disjoint Connectivity: k 2 and 3Number of Hops for Neighborhood in DATC: h 1 and 2Confidence Level 95%

5.2 Experimental Setup

In our experiments, the sensors are randomly deployed in a 600 m × 600 m area. The supern-odes are also randomly and uniformly deployed in this area. The path loss exponent for thewireless channel α is chosen to be 2 and the initial maximum transmission range Rmax of thenodes is set to be 100 m. Since it is required to have a network topology where each sensoris at least k-vertex connected to the set of supernodes, topologies that do not satisfy this con-dition are discarded. For the parameters k and h we use similar values with [51], which aretypical values seen in k-connectivity studies. The experiments are repeated at least hundredtimes for each parameter set and average values are reported at 95% confidence level with amaximum 5% confidence interval. Confidence intervals for reported values are depicted onthe corresponding charts. Our simulation parameters are summarized in Table 5.1.

We assume that each node in the network has a unique ID and no collisions or retransmissionsoccur during wireless communications. We extend our simulations with packet loss scenariosin Section 5.3.6. In addition, we assume that nodes can predict the length of the links usingreceived signal strength. We do not target a specific sensor node technology in the simulations,but it can be considered as any sensor node platform capable of adjusting transmit powerwith a maximum attainable range Rmax of 100 m. As supernodes we consider actor deviceswith dual radios, one for communicating with sensors and one with other supernodes. Themaximum transmission range for supernodes to communicate with sensor nodes is set to be100 m as well. Transmission range for supernodes to communicate with other super nodes isirrelevant for our purpose, but we assume that range to be sufficiently large to communicatewith any other supernode in the network. For sensor nodes, the transmit power needed totalk to a receiver in range is calculated by assuming a simple path loss model and using thesimple formula pi = rαi , as done in [51]. Here, pi is the transmit power node i is using, ri isthe transmission range of the node, and α is the path loss exponent. Hence, the power valuesare simply expressed as a function of the transmission range (i.e., distance) for the purpose ofcomparing the algorithms. Therefore, we do not give power values in a specific energy unitsuch as Joule. We focus mainly on the following metrics to evaluate our algorithms:

• Total transmission power: This is the sum of final transmission power values of eachsingle node in the resulting topology after the execution of the given topology controlalgorithm. This metric is directly related to transmission power cost for communicationin the resulting network and hence an important performance metric for the evaluation

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of the algorithms.

• Maximum transmission power: This is the maximum of final transmission power as-signed among all sensor nodes in the resulting topology after the execution of the giventopology control algorithm. This metric is an indication of how the power consumptionis balanced in the resulting network topology. If an algorithm produces a topology witha high maximum transmission power, that means some nodes will die earlier than theother nodes and hence the network may get disconnected or partitioned in early stagesof the network lifetime.

• Total number of links: This is the sum of the number of the links between the sensornodes in the resulting topology. This metric is related with the total reception powercost of the resulting network topology. Although this metric is not considered in [51],we believe that it is important because number of receptions is also important withrespect to power efficiency of the resulting topology.

• Number of Total Transmissions: This is the sum of number of messages transmittedduring the execution of the algorithms. This metric depicts the transmission power costof generating the k-vertex supernode connected topology. In [51], power consumptionduring the execution of the DATC algorithm is not considered. They only considerthe power consumption of the final topology but it is clear that power consumption ofthe algorithms should also be taken into account, since it directly affects the remainingenergy levels of the sensor nodes in the network.

• Number of Total Receptions: This is the total number of received messages by thesensor nodes in the network during the execution of the algorithms. This metric depictsthe power used during the reception of the messages while generating the final topology.Although number of total transmissions constitutes the essential part of the total powerconsumption, number of receptions may have an important impact on the total powerconsumption. Hence we also monitored this metric in our experiments.

Before going into detailed analysis of the experiment results, we present resulting topologiesafter the execution of the algorithms DATC, DPV and GATC on a sample initial topologyfor 2-vertex disjoint connectivity. The initial network topology shown in Figure 5.1 has 200sensor nodes and 10 supernodes deployed on a 600m x 600m area with an average nodedegree of 8.75.

Figure 5.2 shows the result of execution of DATC algorithm with h=1. It achieves a 30%improvement on the total transmission power where DATC algorithm with h=2 yields a 65%improvement compared to initial topology. The resulting topology after the execution ofDATC algorithm with h=2 is given in Figure 5.3.

The topology generated by our algorithm DPV is illustrated in Figure 5.4. DPV performsbetter than both of the DATC algorithms and achieves a 73% decrease on the total transmissionpower according to the initial topology.

Finally centralized GATC algorithm which produces the optimal result achieves 84% im-provement on the total transmission power. The topology generated by GATC algorithm isshown in Figure 5.5. Note that our distributed algorithm performs fairly close to the optimumresult that is achieved by the centralized GATC algorithm in this case. During the detailedanalysis of the experiment results,we will see that this is not just a coincidence and it is actu-ally the case in general.

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Figure 5.1: Initial sample topology with 200 sensor and 10 supernodes.

5.3 Results

5.3.1 Total Transmission Power

In this section we report experiment results which show the total transmission power of thesensor nodes in the resulting topologies after the execution of GATC, DATC with 1-hop lo-cal neighborhood, DATC with 2-hop local neighborhood and our algorithm DPV. Results ofGATC algorithm is presented as a reference point, since it assigns the optimal transmissionpower to sensor nodes. However note that GATC is a centralized algorithm which requiresglobal knowledge of network topology.

In Figure 5.6(a) and Figure 5.6(b), we present the resulting total transmission powers of thealgorithms with k=2. In Figure 5.6(a) we see that number of sensor nodes goes from 100to 500, where number of sensor nodes is set to 5% of number of sensor nodes. We see thattotal transmission power of the topologies that are generated by DPV is much lower thanthat of DATC(h=1) and DATC(h=2). This shows that the link elimination approach utilizedby DATC has difficulties in discovering alternative disjoint paths to a long direct edge usinglocal data gathered from 1 or 2-hop neighborhood, as we discussed in Section 3. Since thesearch scope is limited, long, hence, costly edges can not be substituted with cheaper disjointpaths, resulting long transmission ranges and thus high total transmission power. Another im-portant observation related to limited search scope is that DATC(h=1) performs significantlyworse than DATC(h=2) which has a broader search scope. However, as will be seen in later

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Figure 5.2: Topology generated by DATC algorithm with h = 1.

figures, DATC(h=2) requires significantly more control message transmissions compared toDATC(h=1) for maintaining 2-hop neighborhood.

Figure 5.6(b) shows the results of our experiments where the number of supernodes is 10% ofnumber of sensor nodes. In Figure 5.6(b), we see almost the same picture as in Figure 5.6(a),except that the total power values are little lower because, due to the high number of supern-odes in the network, it is more likely that cheaper paths will be found. Our DPV algorithmperforms parallel to GATC and the difference between DPV and DATC(h=2) becomes cleareras the network gets denser.

Figure 5.6(b) shows the results of our experiments where the number of supernodes is 10% ofnumber of sensor nodes. In Figure 5.6(b), we see almost the same picture as in Figure 5.6(a),except that the total power values are little lower because, due to the high number of supern-odes in the network, it is more likely that cheaper paths will be found. Our DPV algorithmperforms parallel to GATC and the difference between DPV and DATC(h=2) becomes cleareras the network gets denser.

Figures 5.7(a) and 5.7(b) depict the total transmission power of the topologies generated bythe algorithms for k = 3. We see that the total transmission power of the topologies generatedby DPV is significantly lower than that of DATC(h=1) and DATC(h=2). For k = 3, it is harderto substitute a high cost edge with a low cost one because three disjoint paths are needed tobe able to do that. DATC needs to find these paths in its reachable neighborhood where ouralgorithm can directly search for paths using information in the path vectors. Therefore, ouralgorithm can achieve lower total transmission power compared to DATC. We also observe

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Figure 5.3: Topology generated by DATC algorithm with h = 2.

that satisfying 3-vertex disjoint supernode connectivity requires more transmission power thansatisfying 2-vertex disjoint supernode connectivity in general, as expected.

5.3.2 Maximum transmission power

In this section, we report our experiment results on maximum transmission power among allsensors in the resulting topologies generated by the DATC, DPV and GATC algorithms. Max-imum transmission power is an important metric for the resulting topologies because it is anindication of the balance of energy consumption among all sensors. Even if total transmis-sion power is low, the resulting topology may become disconnected or even partitioned if themaximum transmission power is high because sensor nodes with a high transmission rangewill use more energy than other nodes and deplete their batteries sooner.

Figures 5.8(a) and 5.8(b) show the maximum transmission powers of the topologies generatedby the algorithms for k = 2, where the number of supernodes is 5% and 10% of the sensornodes, respectively. We observe that GATC produces topologies with the lowest maximumtransmission power among all algorithms. This is due to the fact that GATC is a centralizedalgorithm and has global network topology information. Thus it directly knows where thelongest edges reside in the network and eliminates edges in the order of decreasing cost whenpossible. The DPV and DATC algorithms, on the other hand, are localized algorithms andhave a partial knowledge of the network topology. For that reason, they generate topologieswith higher maximum transmission power compared to GATC. Our proposed DPV algorithm

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Figure 5.4: Topology generated by our algorithm DPV.

has the next best performance, which is significantly better than the DATC algorithms. Thisresult is again related to the available information for discovering disjoint paths. DATC canobtain limited information compared to DPV, therefore it cannot discover as many disjointpath as our DPV algorithm. This results higher maximum transmission ranges for DATC.DATC(h=1) seems to make almost no improvement on maximum transmission power andDATC(h=2) performs only slightly better.

For k = 3, Figures 5.9(a) and 5.9(b) show the comparison of maximum transmission powersfor the resulting topologies. The results are similar to when k = 2 except that maximumtransmission power values are greater. This is an expected result because keeping the network3-connected requires keeping more neighbors connected, which leads to higher transmissionranges for the sensor nodes.

5.3.3 Total number of links

In this section we present the experiment results regarding the total number links after theexecution of each topology control algorithm being compared. Smaller number of links meanslower number of receptions due to a transmission. Beside the transmission, message receptionalso consumes energy so it is important to decrease the number of receptions and hence thenumber of total links.

Figures 5.10(a) and Figure 5.10(b), show the resulting number of links after the execution of

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Figure 5.5: Optimum topology generated by GATC algorithm.

each algorithms with k=2.

In Figure 5.10(a) number of sensor nodes goes from 100 to 500, where number of sensornodes is set to 5% of number of sensor nodes. We see that total number of links in thetopologies that are generated by DATC(h=1) are increasing very fast while the network sizeis increasing. DPV results less number of links than both of the DATC algorithms. Numberof links for both DPV and GATC increase slowly while the number of nodes is increasing.GATC performs slightly better than DPV, and DPV performs slightly better than DATC(h=2).So we can say that topologies generated by DATC algorithm will consume more power forreception than that of DPV. Another observation is that DATC(h=2) produces less number oflinks than DATC(h=1) as expected.

In Figure 5.10(b) when supernodes is 10%, we see almost the same picture as in Figure 5.10(a)in terms of relative behaviors of the algorithms.

Figures 5.10(a) and Figure 5.10(b), show the resulting number of links after the execution ofeach algorithm with k=3. We observe the same pattern with the case where k=2, but herewe see that we need more links to keep the sensors 3-vertex disjoint path connected to set ofsupernodes. We can infer this by comparing the behavior of DPV in cases where k=2 andk=3. When k=2, and number of sensor nodes is 500, approximately 1000 links are enough tomaintain the 2-vertex connectivity. On the other hand when k=3, we need approximately 1400links to keep the network 3-vertex connected to supernodes. Same behavior is also observedfor the other algorithms.

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5.3.4 Total Number of Control Message Transmissions

In this section we give and discuss our experiment results regarding the total number of con-trol message transmissions during the execution of the DPV and DATC algorithms. GATCdoes not require control message transmissions while computing the topology, since the com-putation is done centrally. Control message transmission metric is important because it isnecessary not only to consider power consumption in the resulting topologies but also to con-sider the power consumption required to generate those topologies, which can be viewed asa fixed cost of obtaining the final topologies. If this cost is high, then the power efficiency ofthe resulting topology might become meaningless.

In Figures 5.12(a) and 5.12(b), we present the total number of required control message trans-missions to execute the algorithms with k = 2. The most important observation here is thatDATC(h=2) requires an asymptotically larger number of transmissions than DATC(h=1) orDPV, because in DATC(h=2) each node needs to notify all nodes in its 2-hop neighbor-hood. While DATC(h=1) and DPV require only one message transmission for an update,DATC(h=2) requires ∆ transmissions, where ∆ is the degree of a given sensor node. This sit-uation shows that DATC(h=2) may not be feasible in practice, because transmitting so manymessages during algorithm execution will cause rapid battery drain. Therefore, extendingthe DATC algorithm for more than 1-hop neighborhood seems not to be scalable due to theexponentially increasing number of update messages.

As another benefit, DPV requires fewer transmissions than DATC(h=1) to obtain a k-vertexdisjoint connected network topology. This is expected because DPV transmits an updatemessage only if a set of disjoint paths with a lower cost is discovered whereas DATC sendsupdate messages in all power increments. Due to smaller search scope, DATC is often unableto find disjoint paths and thus the number of power increments tends to be high.

In Figures 5.13(a) and 5.13(b), we present the total number of required control message trans-missions to execute the algorithms with k = 3. The behaviors of all three algorithms are similarwith k = 2, except when k = 3 all algorithms require slightly more message transmissions.

5.3.5 Total Number of Control Message Receptions

Another factor that has an impact upon power efficiency is the total number of received mes-sages during the execution of the topology control algorithms. This is again a fixed cost as inthe case of total transmissions required.

Figures 5.14(a) and 5.14(b) show the total number of received control messages during theexecution of the algorithms with k = 2, and Figures 5.15(a) and 5.15(b) show the same for k= 3. Here again we observe that during the execution of DATC(h=2) many more receptionsoccur compared to DATC(h=1) and DPV in all cases. This is a direct result of high numberof transmissions required by DATC as discussed in Section 5.3.4.

We observe that when the number of supernodes is 5% of the sensor nodes and k = 2, DPVrequires fewer receptions than DATC(h=1). In all other cases the total number of receivedmessages for DPV and DATC(h=1) is almost the same. For all algorithms, number of re-ceptions tend to increase when k and the number of supernodes increase, but the increasefor DATC(h=2) is significantly faster than that of DPV and DATC(h=1). Another important

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observation is that the number of receptions is about five times greater than the number oftransmissions. This result is expected because when a message is transmitted it is received bymultiple nodes in the 1-hop neighborhood.

5.3.6 Effect of Packet Losses

In wireless transmission medium packet losses are frequent due to collisions, link errors andenvironmental conditions. In order to justify our results, we present an additional scenariowhere packet losses can occur randomly in any link in the network with a given probability.In this scenario, retransmissions are also considered and maximum number of retransmissionsis set to be 3. We change the packet loss ratio (PLR) between 0.1 and 0.4 with 0.1 steps andpresent the effect of packet losses on total transmission power in Figures 5.16(a), 5.16(b),5.17(a) and 5.17(b).

We observe that when PLR increases total transmission power also increases. This is an ex-pected result because under a higher PLR, a higher number of information exchange messagesare lost and thus nodes can obtain an incomplete topology information from their neighbors.Using this partial information all three algorithms miss some of the more efficient paths be-cause messages carrying that information were lost due to communication faults.

As seen in Figures 5.16(a) and 5.16(b), our algorithm DPV performs better than DATC(h=1)and DATC(h=2) as in the previous scenarios without packet loss consideration. However wesee that the reduction in total power is not as high as in the previous scenario, it drops to 30%when PLR is 0.2. When PLR is 0.3 and higher DATC(h=2) starts to perform better than ouralgorithm in terms of total transmission power of the final topologies. This is due to the factthat DATC algorithms are more localized than DPV because they only use 1-hop or 2-hopneighborhood information which means their messages go only 1 or 2-hops. On the otherhand DPV algorithm gathers path information from a wider area where messages can traverseup to the predefined TTL value which is typically 6 or 7. Since messages traverse longerpaths in the DPV algorithm, these messages are more prone to packet losses. To elaborate,succesful delivery chance of a message over a 2-hop path is 3 times higher compared to a5-hop path when PLR is 0.3. However a PLR ratio as high as 0.3 per link is not realistic. In[7] it is reported that between 0 and 70 meters the average PLR is under 0.1 for CrossbowIRIS mote. In addition, total number of control message transmissions for DATC(h=2) ismuch higher than DPV due to the need of power update messages in 2-hop neighborhood asseen in Figures 5.18(a), 5.18(b), 5.19(a) and 5.19(b). DATC(h=1) still results with the highesttotal transmission power due to its limited search scope as discussed in 5.3.1. Therefore wecan conclude that under realistic PLR values, our algorithm DPV still outperforms DATCalgorithms in terms of total transmission power and total number of transmissions.

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CHAPTER 6

CONCLUSION

Wireless sensor networks (WSNs) have been widely recognized as a promising technologyand studied extensively for their advantages over traditional communication technologies in-cluding their low cost and easy deployment without any infrastructure. However, WSNs havetheir unique challenges and requirements such as energy efficiency and fault-tolerant oper-ation. Recent studies have revealed that heterogeneous WSNs, where the network consistsof different kind of sensors can result better energy efficiency and a higher fault tolerancecompared to homogeneous wireless sensor networks [59]. In this work, we focus on hetero-geneous two-layered network architectures where the lower layer consists of ordinary sensornodes and the upper layer consists of resource-rich supernodes. In such topologies, sensornodes forward their data towards supernodes using multi-hop paths. Supernodes collect andprocess the incoming data and can make critical decisions based on the application. For somescenarios, data delivery can be critical, so a fault-tolerant topology would be essential whereeach node has a certain degree of connectivity to the set of supernodes.

In this thesis, we introduce a new distributed algorithm, called the DPV (Disjoint Path VectorAlgorithm), for constructing fault-tolerant topologies for heterogeneous wireless sensor net-works consisting of supernodes and ordinary sensor nodes. There are many topology controlalgorithms in literature for ad hoc and wireless sensor networks as discussed in Section 2.3and Chapter 3. However, not all of these algorithms consider fault tolerance which is a crit-ical requirement for wireless sensor network applications. In addition, most of the existingtopology control algorithms target connectivity between any two nodes in the network, buttypically the connectivity between sensor nodes and the sink nodes is important for most ofthe WSN applications. Also, we noticed that there are a few topology control algorithmsfor layered network architectures where each layer consists of different type of sensor nodes.With this thesis we contribute with the DPV algorithm, which fulfills all the requirementsmentioned above.

The DPV algorithm results in topologies where each sensor node in the network has at leastk-vertex disjoint paths to the supernodes provided that the given network topology is k-vertexsupernode connected. The objective of the algorithm is to minimize the total transmissionpower of the nodes in the network. The DPV algorithm is run by each sensor in a distributedmanner with locally collected data. Using this data each node computes the set of requiredneighbors that guarantees k-vertex supernode connectivity. The changes in the neighbor listsare exchanged in an efficient way to keep the message overhead small. We showed that thegenerated topologies are k-vertex supernode connected and bidirectional with formal proofsin Section 4.5.

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We evaluate our algorithm using a custom simulator that we developed, which enables gen-erating random network topologies, executing the algorithms on generated topologies, cal-culating the desired metrics and visualizing the outputs of the experiments. We have im-plemented the DPV, GATC and DATC algorithms using this simulator and we compare theresults, namely, total transmission power and maximum transmission power among all thesensors in the resulting topologies generated by each algorithm, as well as the number oftotal transmissions and receptions required for executing the algorithms. The simulation re-sults show that our approach outperforms the existing distributed algorithms in all aspects.Compared to existing solutions, our DPV algorithm achieves a 4-fold reduction in total trans-mission power and a 2-fold reduction in maximum transmission power. Under realistic packetloss scenarios our algorithm results with 60% decrease in total transmission power. In otherwords, topologies generated by our algorithm use up to four times less power compared totopologies generated by the existing algorithms. In addition, our algorithm achieves these re-sults by requiring fewer message transmissions and receptions. The most important contribu-tion of the DPV algorithm is to generate topologies that have total transmission powers closeto optimum, i.e., that is achieved by the centralized GATC algorithm. As mentioned before,the GATC is a centralized algorithm and requires global network information. Therefore it isless practical for large-scale networks. The solution we propose is, however, distributed andlocalized, thus is scalable to large networks and therefore suitable for use in real applications.

Future work could construct power-balanced topologies, which could be achieved by con-sidering the remaining energy levels of sensor nodes while selecting the required neighbors.Such a topology would be more stable because it would prevent early node failures due toenergy depletion.

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CURRICULUM VITAE

PERSONAL INFORMATION

Surname, Name: Bagcı, HakkıNationality: Turkish (TC)Date and Place of Birth: 23-Feb-1982, BeypazarıMarital Status: MarriedPhone: +90 506 541 65 57E-Mail: [email protected]

EDUCATION

Degree Institution Year of GraduationM.S. Bilkent University, Computer Engineering 2007B.S. Bilkent University, Computer Engineering 2004

PROFESSIONAL EXPERIENCE

Year Place Enrollment2013 - ... TUBITAK / BILGEM / ILTAREN Chief Researcher2009 - 2013 TUBITAK / BILGEM / ILTAREN Senior Researcher2004 - 2009 TUBITAK / BILGEM / ILTAREN Researcher

PUBLICATIONS

International Journal Publications

Hakki Bagci and Ibrahim Korpeoglu, Distributed and Location Based Multicast Routing Al-gorithms for Wireless Sensor Networks. EURASIP Journal on Wireless Communications andNetworking, vol. 2009, Article ID 697373, 14 Pages, 2009.

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